Fix #10110: sphinx-build: Emit builder-finished before shutdown

The error on the builder-finished event has been ignored for the
calculation of the exit code.  This emits the event earilier step to be
calculated correctly.

CHANGES

@@ -16,6 +16,9 @@ Features added
 Bugs fixed
 ----------
 
+* #10110: sphinx-build: exit code is not changed when error is raised on
+  builder-finished event
+
 Testing
 --------
 

sphinx/application.py

@@ -328,6 +328,15 @@ class Sphinx:
                 self.builder.compile_update_catalogs()
                 self.builder.build_update()
 
+            self.events.emit('build-finished', None)
+        except Exception as err:
+            # delete the saved env to force a fresh build next time
+            envfile = path.join(self.doctreedir, ENV_PICKLE_FILENAME)
+            if path.isfile(envfile):
+                os.unlink(envfile)
+            self.events.emit('build-finished', err)
+            raise
+
         if self._warncount and self.keep_going:
             self.statuscode = 1
 
@@ -355,15 +364,7 @@ class Sphinx:
                 'outdir': relpath(self.outdir),
                 'project': self.config.project
             })
-        except Exception as err:
-            # delete the saved env to force a fresh build next time
-            envfile = path.join(self.doctreedir, ENV_PICKLE_FILENAME)
-            if path.isfile(envfile):
-                os.unlink(envfile)
-            self.events.emit('build-finished', err)
-            raise
-        else:
-            self.events.emit('build-finished', None)
+
         self.builder.cleanup()
 
     # ---- general extensibility interface -------------------------------------