None of my groups are listed on the Manage Groups option in the Contacts menu. Its applies to all my sites which vary between CiviCRM 5.2 to 5.11. Some are new sites some upgraded from 4.7.x where it worked fine as far as I can remember. The groups are there (for example in a drop down in Find Contacts). I can add a new group, but that doesn't show in the listing either. Also there is no search button on the Find Groups part of the page (it is there in the documentation).
I tried the WordPress sandpit demo and that is the same (though most of the menus are missing (but fortunately Manage Groups was there) so it looks a bit odd and on the Drupal sandpit I couldn't see any menu, so couldn't try there). Nothing in the CiviCRM log at the time I tried.
I'm using WordPress 5.1 and CiviCRM 5.2 to 5.11 on various sites.