FIX: Don't load all groups when rendering <GroupChooser /> (#31271)

In a few places throughout the app, when we render the `<GroupChooser
/>` component, we fetch the full groups list of the site from the
`/groups/search` endpoint. This is wasteful because the full groups list
is already included in the preloaded data that's sent to the client app
on the initial page load, so we can just use this preloaded list for
`<GroupChooser />` and we can avoid making an HTTP request.

Internal topic: t/147297.

spec/requests/api/schemas/json/site_response.json

@@ -288,6 +288,11 @@
                 "string",
                 "null"
               ]
+            },
+            "automatic": {
+              "type": [
+                "boolean"
+              ]
             }
           },
           "required": [
@@ -295,7 +300,8 @@
             "name",
             "flair_url",
             "flair_bg_color",
-            "flair_color"
+            "flair_color",
+            "automatic"
           ]
         }
     },