Copy-Paste from Firefox 88.0.1 not working properly on Ubuntu 21.04 (Hirsute Hippo)
Solution 1:
Ubuntu 21.04 uses Wayland by default, try to log out and make sure you are login using the Xorg/Xserver.
In the login page, look for an option to select which session you like to use. see this example pic 
Solution 2:
So to answer your question
Any idea what's going on?
Firefox has reoccurring bugs when using it under Wayland (i.e. on modern Ubuntu or Fedora):
- 1438136
- 1485916
- 1567762
- 1622538
- 1631061
- 1636712
So you might follow these issues to be notified once it is fixed.
Until then you might indeed have to use X11 instead of Wayland.