Per T108630, HotCat is currently broken on many wikis that have local copies of the old gadget code (rather than importing the code from Commons). We should identify the wikis that have local copies, and fix them.
To identify the wikis where it is broken, we could run a bot to check MediaWiki:Gadget-HotCat.js on each wiki and see if it is more than a few lines long, which generally means there is a local version of the Gadget (which is probably broken).