This actually caught me out just as I was uploading! Did almost all the development for the game in Firefox on Linux, but seems like there's a specific issue with itch and godot mouse capture. I added a comment to an issue I found on GitHub about it - if there are any developments I'll update: https://github.com/godotengine/godot/issues/51810
(In the meantime, it worked for me when I played in fullscreen, at least)