Same problem here. (Pico W)
I think it's a UI problem only.
It's well known, that pico can cause problem, as it just disappears from the system when the file uploading has finished.
I'm just guessing, but I think at the end of the upload, the process try to close the connection to the filesystem, that is not presented (pico are already rebooting), what cause an exception with the UI process... Everything is fine, but the popup not closed, and the button can not be pressed again.
My config: UF2 board selected for at tools/port and Default uf2 selected at Tools/Upload method.
Let me know if I can provide any more information!