Add ONLY_SHOW_RELEVANT_REPOS back, fix explore page bug, make code more strict (#23766)

Follow #21962

After I eat my own dogfood, I would say that
ONLY_SHOW_RELEVANT_REPOS=false is necessary for many private/enterprise
instances, because many private repositories do not have
"description/topic", users just want to search by their names.

This PR also adds `PageIsExploreRepositories` check, to make code more
strict, because the `search` template is shared for different purpose.

And during the test, I found a bug that the "Search" button didn't
respect the "relevant" parameter, so this PR fixes the bug by the way
together.

I think this PR needs to be backported.

docs/content/doc/administration/config-cheat-sheet.en-us.md

@@ -226,11 +226,13 @@ The following configuration set `Content-Type: application/vnd.android.package-a
     Values can be emoji alias (:smile:) or a unicode emoji.
     For custom reactions, add a tightly cropped square image to public/img/emoji/reaction_name.png
 - `CUSTOM_EMOJIS`: **gitea, codeberg, gitlab, git, github, gogs**: Additional Emojis not defined in the utf8 standard.
-    By default we support Gitea (:gitea:), to add more copy them to public/img/emoji/emoji_name.png and
+    By default, we support Gitea (:gitea:), to add more copy them to public/img/emoji/emoji_name.png and
     add it to this config.
 - `DEFAULT_SHOW_FULL_NAME`: **false**: Whether the full name of the users should be shown where possible. If the full name isn't set, the username will be used.
 - `SEARCH_REPO_DESCRIPTION`: **true**: Whether to search within description at repository search on explore page.
 - `USE_SERVICE_WORKER`: **false**: Whether to enable a Service Worker to cache frontend assets.
+- `ONLY_SHOW_RELEVANT_REPOS`: **false** Whether to only show relevant repos on the explore page when no keyword is specified and default sorting is used.
+    A repo is considered irrelevant if it's a fork or if it has no metadata (no description, no icon, no topic).
 
 ### UI - Admin (`ui.admin`)