Unfortunately I cannot reproduce this issue.
I have created a new document in my home directory using Thunar and copied it across via the command line ("sudo cp ~/Test.txt /usr/share/") without any issues. I could also copy-and-paste it across when I opened Thunar as root.
Are you doing anything differently?

@re4son (not sure how replying works on this platform) You do appear to be doing something different from me, as you are using window mode, instead of the stemless mode that I am observing this issue with. To enter seamless mode, kill all kex processes by running kex --kill, then launch into seamless mode by doing kex --sl (It appears i mistyped the command in the steps to reproduce, sorry about that). I did try doing the same operation as I described but in window mode, and it doesn't crash kex, instead it pops up a permission denied error from the file progress window, which is the expected behavior. I wonder if this is an issue with all dialog boxes, or just this one on the file progress bar. Something to look into further.

Interesting find. Thanks for letting us know. It might be related to a critical error when trying to resize the window of the error message.
Seems to be a bug in the X-Server we are using and not much we can do except trying not to cause error messages in thunar.
Here's a tip:

No need to use Win-KeX SL on Windows 11. Just create a shortcut to the application finder in your quick start bar and use WSLg.
Microsoft have integrated Win-KeX SL into Windows 11 ;-)