X11 or Wayland?

Did you try Firefox in Safe Mode? https://support.mozilla.org/en-US/kb/diagnose-firefox-issues-using-troubleshoot-mode#search104

Try downloading Firefox from Mozilla, run firefox-bin from the folder and see if you have the same issue. https://www.mozilla.org/en-US/firefox/all/#product-desktop-release

I think the display server in Ubuntu 23.04 is Wayland, based on: https://wiki.debian.org/Wayland#Firefox_.28supported.29

Also, I need to make a correction: It's the Ubuntu user session that crashes because I get back to the user login.

The session still crashed after I tried: (a) after the Safe mode & (b) after downloading from the site suggested & (c) after safe-mode & renaming the Firefox preference file: prefs.js as mentioned in the first link above.

What happens in X11?

Switching ti X11 worked. It's easy. On the Ubuntu login screen, tab to the gear icon on bottom right, enter & select: 'Ubuntu' (Wayland) or 'Ubuntu with Xorg'. Then one can joyfully frolic moving around ff tabs :)

I think I'm having the same problem (in my case trying to drag a tab to another monitor), and switching to X11 does fix it. Is there a bug report or something I can subscribe to that will let me know when the problem between Firefox/Ubuntu/Wayland is fixed?