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.