Not really sure what to do here then.
I just used simplytest.me and spun up an install of Drupal 11.1.2. (I was running into dependency issues trying to build with Devel in the mix, so just used a basic install and manually created 50 menu entries.)
Using my test steps above, I was able to replicate that this is indeed happening in D11 (as well as D10) - once enough menu entries exist to trigger pagination (screenshot attached).
@oily I have updated the test steps in the original description. I walked through these steps using simplytest.me and was able to produce the screen capture. Please let me know if further clarification is required.
We use Composer so adding a patch file for easier local testing.
I haven't been able to determine a root cause for us. Since this appears to be an 'us' issue and we'll be updating to Drupal 10 soon (where it seems to work again) I think it is safe to just close this support ticket. Thanks!
Oh, interesting. I'm seeing the issue on our Drupal 9.5.11 sites, and even a simple vanilla Docker instance running Bitnami Drupal 9.5.11 that I set up strictly for testing Gin. It works fine for RC3, but anything after and it stops working for us. I'm just not seeing the is-sticky class (or the newer data-drupal-sticky-vbo="true") being set when expected.
But with your feedback, I spun up a simplytest.me instance and can indeed see it working there as expected.
I'll do some more poking about to see if I can suss out the source of our issue. Thanks.