In the content type display manage page cannot see the view mode tab

I've just tested this using the latest Drupal 10 and 11 releases and can't reproduce this. Make sure the blocks are set. Maybe try reinstalling Gin to see if that fixes the issue (this will recreate the needed blocks).

I hope this helps, Cheers!

The bug only appears in Drooper; when I use other management themes in Drooper, there are no issues.

I'd suggest to report this to Droopler then! :)

I have already done so, thank you.

Reinstall gin is work.