I recently came upon this problem. On Ventura - but a Google suggests this is not limited to that OS. I'd get the 'Emptying the Trash...' window as above, but then it would just stay there, while clicking the [X] would complete action and close window. Just as you describe.
Anyway, one of the searches suggested going to System Settings > General > Login Items > Open at Login. Make a note of what is in that section (so that you can add them back later, if necessary), and then try deleting one at a time, with a reboot between each. Then try to Empty Trash as normal (I created a doc and then move it to Trash just for that purpose). If it works as expected, you may have found the culprit.
I got lucky with first guess - turns out it was a Dropbox login that caused the problem. Not sure why. I know there had been 'improvements' made to Dropbox recently, but I'm happy to kill it off at login. Interestingly (or maybe just coincidentally), one of the Google threads I found was saying that it was a OneDrive login causing the issue. So maybe these cloud service links are the first thing to look at here?