diff --git a/pyproject.toml b/pyproject.toml
index 9e3f4df91..12701fe7e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -87,6 +87,7 @@ lint = [
     "sphinx-lint",
     "docutils-stubs",
     "types-requests",
+    "pytest>=6.0",
 ]
 test = [
     "pytest>=6.0",
@@ -133,9 +134,6 @@ exclude = [
 files = ["sphinx"]
 check_untyped_defs = true
 disallow_incomplete_defs = true
-follow_imports = "skip"
-ignore_missing_imports = true
-no_implicit_optional = true
 python_version = "3.9"
 show_column_numbers = true
 show_error_context = true
@@ -152,6 +150,9 @@ enable_error_code = [
     "ignore-without-code",
     "unused-awaitable",
 ]
+disable_error_code = [
+    "import-untyped",
+]
 
 [[tool.mypy.overrides]]
 module = [
diff --git a/sphinx/ext/autosummary/generate.py b/sphinx/ext/autosummary/generate.py
index 9ebb0cfb9..b7668894a 100644
--- a/sphinx/ext/autosummary/generate.py
+++ b/sphinx/ext/autosummary/generate.py
@@ -133,7 +133,8 @@ class AutosummaryRenderer:
 
         if app.translator:
             self.env.add_extension("jinja2.ext.i18n")
-            self.env.install_gettext_translations(app.translator)
+            # ``install_gettext_translations`` is injected by the ``jinja2.ext.i18n`` extension
+            self.env.install_gettext_translations(app.translator)  # type: ignore[attr-defined]
 
     def render(self, template_name: str, context: dict) -> str:
         """Render a template file."""
diff --git a/sphinx/jinja2glue.py b/sphinx/jinja2glue.py
index 652180015..e8c0c942f 100644
--- a/sphinx/jinja2glue.py
+++ b/sphinx/jinja2glue.py
@@ -8,17 +8,12 @@ from typing import TYPE_CHECKING, Any, Callable
 
 from jinja2 import BaseLoader, FileSystemLoader, TemplateNotFound
 from jinja2.sandbox import SandboxedEnvironment
-from jinja2.utils import open_if_exists
+from jinja2.utils import open_if_exists, pass_context
 
 from sphinx.application import TemplateBridge
 from sphinx.util import logging
 from sphinx.util.osutil import mtimes_of_files
 
-try:
-    from jinja2.utils import pass_context
-except ImportError:
-    from jinja2 import contextfunction as pass_context
-
 if TYPE_CHECKING:
     from collections.abc import Iterator
 
@@ -194,7 +189,9 @@ class BuiltinTemplateLoader(TemplateBridge, BaseLoader):
         self.environment.globals['accesskey'] = pass_context(accesskey)
         self.environment.globals['idgen'] = idgen
         if use_i18n:
-            self.environment.install_gettext_translations(builder.app.translator)
+            # ``install_gettext_translations`` is injected by the ``jinja2.ext.i18n`` extension
+            self.environment.install_gettext_translations(  # type: ignore[attr-defined]
+                builder.app.translator)
 
     def render(self, template: str, context: dict) -> str:  # type: ignore[override]
         return self.environment.get_template(template).render(context)
@@ -218,5 +215,6 @@ class BuiltinTemplateLoader(TemplateBridge, BaseLoader):
                 return loader.get_source(environment, template)
             except TemplateNotFound:
                 pass
-        msg = f"{template!r} not found in {self.environment.loader.pathchain}"
+        msg = (f"{template!r} not found in "
+               f"{self.environment.loader.pathchain}")  # type: ignore[union-attr]
         raise TemplateNotFound(msg)
diff --git a/sphinx/registry.py b/sphinx/registry.py
index 1ea6b1a01..62d1e3e5c 100644
--- a/sphinx/registry.py
+++ b/sphinx/registry.py
@@ -11,7 +11,7 @@ from typing import TYPE_CHECKING, Any, Callable
 if sys.version_info >= (3, 10):
     from importlib.metadata import entry_points
 else:
-    from importlib_metadata import entry_points
+    from importlib_metadata import entry_points  # type: ignore[import-not-found]
 
 from sphinx.domains import Domain, Index, ObjType
 from sphinx.domains.std import GenericObject, Target
diff --git a/sphinx/search/ja.py b/sphinx/search/ja.py
index 18aa12f99..5669155cb 100644
--- a/sphinx/search/ja.py
+++ b/sphinx/search/ja.py
@@ -13,16 +13,16 @@ from __future__ import annotations
 import os
 import re
 import sys
-from typing import TYPE_CHECKING, Any, Dict, List
+from typing import Any
 
 try:
-    import MeCab
+    import MeCab  # type: ignore[import-not-found]
     native_module = True
 except ImportError:
     native_module = False
 
 try:
-    import janome.tokenizer
+    import janome.tokenizer  # type: ignore[import-not-found]
     janome_module = True
 except ImportError:
     janome_module = False
diff --git a/sphinx/search/zh.py b/sphinx/search/zh.py
index b3a0e77f7..e40c9a9fe 100644
--- a/sphinx/search/zh.py
+++ b/sphinx/search/zh.py
@@ -4,14 +4,13 @@ from __future__ import annotations
 
 import os
 import re
-from typing import TYPE_CHECKING, Dict, List
 
 import snowballstemmer
 
 from sphinx.search import SearchLanguage
 
 try:
-    import jieba
+    import jieba  # type: ignore[import-not-found]
     JIEBA = True
 except ImportError:
     JIEBA = False
diff --git a/sphinx/testing/fixtures.py b/sphinx/testing/fixtures.py
index 3f316b664..eaf76e284 100644
--- a/sphinx/testing/fixtures.py
+++ b/sphinx/testing/fixtures.py
@@ -82,7 +82,7 @@ def app_params(request: Any, test_params: dict, shared_result: SharedResult,
     if test_params['shared_result']:
         if 'srcdir' in kwargs:
             msg = 'You can not specify shared_result and srcdir in same time.'
-            raise pytest.Exception(msg)
+            pytest.fail(msg)
         kwargs['srcdir'] = test_params['shared_result']
         restore = shared_result.restore(test_params['shared_result'])
         kwargs.update(restore)
diff --git a/sphinx/theming.py b/sphinx/theming.py
index e95f4c8cc..2a6040e5d 100644
--- a/sphinx/theming.py
+++ b/sphinx/theming.py
@@ -22,7 +22,7 @@ from sphinx.util.osutil import ensuredir
 if sys.version_info >= (3, 10):
     from importlib.metadata import entry_points
 else:
-    from importlib_metadata import entry_points
+    from importlib_metadata import entry_points  # type: ignore[import-not-found]
 
 if TYPE_CHECKING:
     from sphinx.application import Sphinx
diff --git a/sphinx/util/i18n.py b/sphinx/util/i18n.py
index 004b5d85f..ae512bd36 100644
--- a/sphinx/util/i18n.py
+++ b/sphinx/util/i18n.py
@@ -6,7 +6,7 @@ import os
 import re
 from datetime import datetime, timezone
 from os import path
-from typing import TYPE_CHECKING, Callable, NamedTuple
+from typing import TYPE_CHECKING, NamedTuple
 
 import babel.dates
 from babel.messages.mofile import write_mo
@@ -18,10 +18,41 @@ from sphinx.util import logging
 from sphinx.util.osutil import SEP, canon_path, relpath
 
 if TYPE_CHECKING:
+    import datetime as dt
     from collections.abc import Generator
+    from typing import Protocol, Union
+
+    from babel.core import Locale
 
     from sphinx.environment import BuildEnvironment
 
+    class DateFormatter(Protocol):
+        def __call__(  # NoQA: E704
+            self,
+            date: dt.date | None = ...,
+            format: str = ...,
+            locale: str | Locale | None = ...,
+        ) -> str: ...
+
+    class TimeFormatter(Protocol):
+        def __call__(  # NoQA: E704
+            self,
+            time: dt.time | dt.datetime | float | None = ...,
+            format: str = ...,
+            tzinfo: dt.tzinfo | None = ...,
+            locale: str | Locale | None = ...,
+        ) -> str: ...
+
+    class DatetimeFormatter(Protocol):
+        def __call__(  # NoQA: E704
+            self,
+            datetime: dt.date | dt.time | float | None = ...,
+            format: str = ...,
+            tzinfo: dt.tzinfo | None = ...,
+            locale: str | Locale | None = ...,
+        ) -> str: ...
+
+    Formatter = Union[DateFormatter, TimeFormatter, DatetimeFormatter]
 
 logger = logging.getLogger(__name__)
 
@@ -169,7 +200,7 @@ date_format_re = re.compile('(%s)' % '|'.join(date_format_mappings))
 
 
 def babel_format_date(date: datetime, format: str, locale: str,
-                      formatter: Callable = babel.dates.format_date) -> str:
+                      formatter: Formatter = babel.dates.format_date) -> str:
     # Check if we have the tzinfo attribute. If not we cannot do any time
     # related formats.
     if not hasattr(date, 'tzinfo'):
@@ -207,6 +238,7 @@ def format_date(
             # Check if we have to use a different babel formatter then
             # format_datetime, because we only want to format a date
             # or a time.
+            function: Formatter
             if token == '%x':
                 function = babel.dates.format_date
             elif token == '%X':
diff --git a/sphinx/util/rst.py b/sphinx/util/rst.py
index 1e8fd66c7..9f9c3d7cb 100644
--- a/sphinx/util/rst.py
+++ b/sphinx/util/rst.py
@@ -54,7 +54,8 @@ def textwidth(text: str, widechars: str = 'WF') -> int:
 def heading(env: Environment, text: str, level: int = 1) -> str:
     """Create a heading for *level*."""
     assert level <= 3
-    width = textwidth(text, WIDECHARS[env.language])
+    # ``env.language`` is injected by ``sphinx.util.template.ReSTRenderer``
+    width = textwidth(text, WIDECHARS[env.language])  # type: ignore[attr-defined]
     sectioning_char = SECTIONING_CHARS[level - 1]
     return f'{text}\n{sectioning_char * width}'
 
diff --git a/sphinx/util/tags.py b/sphinx/util/tags.py
index 73e1a8308..5d8d8900a 100644
--- a/sphinx/util/tags.py
+++ b/sphinx/util/tags.py
@@ -20,8 +20,8 @@ class BooleanParser(Parser):
     Only allow condition exprs and/or/not operations.
     """
 
-    def parse_compare(self) -> Node:
-        node: Node
+    def parse_compare(self) -> nodes.Expr:
+        node: nodes.Expr
         token = self.stream.current
         if token.type == 'name':
             if token.value in ('true', 'false', 'True', 'False'):
@@ -67,7 +67,7 @@ class Tags:
             msg = 'chunk after expression'
             raise ValueError(msg)
 
-        def eval_node(node: Node) -> bool:
+        def eval_node(node: Node | None) -> bool:
             if isinstance(node, nodes.CondExpr):
                 if eval_node(node.test):
                     return eval_node(node.expr1)
diff --git a/sphinx/util/template.py b/sphinx/util/template.py
index e379a51cc..0ddc29e17 100644
--- a/sphinx/util/template.py
+++ b/sphinx/util/template.py
@@ -26,7 +26,8 @@ class BaseRenderer:
     def __init__(self, loader: BaseLoader | None = None) -> None:
         self.env = SandboxedEnvironment(loader=loader, extensions=['jinja2.ext.i18n'])
         self.env.filters['repr'] = repr
-        self.env.install_gettext_translations(get_translator())
+        # ``install_gettext_translations`` is injected by the ``jinja2.ext.i18n`` extension
+        self.env.install_gettext_translations(get_translator())  # type: ignore[attr-defined]
 
     def render(self, template_name: str, context: dict[str, Any]) -> str:
         return self.env.get_template(template_name).render(context)
diff --git a/sphinx/versioning.py b/sphinx/versioning.py
index 042b97d89..ab1701537 100644
--- a/sphinx/versioning.py
+++ b/sphinx/versioning.py
@@ -18,7 +18,7 @@ if TYPE_CHECKING:
     from sphinx.application import Sphinx
 
 try:
-    import Levenshtein
+    import Levenshtein  # type: ignore[import-not-found]
     IS_SPEEDUP = True
 except ImportError:
     IS_SPEEDUP = False
diff --git a/sphinx/writers/latex.py b/sphinx/writers/latex.py
index c55a211d5..5a4778e48 100644
--- a/sphinx/writers/latex.py
+++ b/sphinx/writers/latex.py
@@ -29,7 +29,7 @@ try:
     from docutils.utils.roman import toRoman
 except ImportError:
     # In Debian/Ubuntu, roman package is provided as roman, not as docutils.utils.roman
-    from roman import toRoman  # type: ignore[no-redef]
+    from roman import toRoman  # type: ignore[no-redef, import-not-found]
 
 if TYPE_CHECKING:
     from docutils.nodes import Element, Node, Text