Q: Should this work on lates linux mint installation? about chatgpt-gnome-desktop-extension

[lupinx2]

This is a Gnome-shell extension and so requires that your OS be using Gnome. From what I know Mint does not have an official Gnome version, so it shouldn't be possible to easily install this on Matte/XFCE. Cinnamon is based on Gnome 3 so it might be a little easier if it can handle Gnome extensions, but keep in mind this extension is intended for Gnome 42+ so it also wouldn't work out of the box even then.

[avma]

Thanks Luis,
I am currently using Mint Cinnamon as my operating system. I have installed all the recommended dependencies and packages mentioned on the project site, but unfortunately, the program is not working properly. There are no error messages, but it simply doesn't seem to be doing anything.

[lupinx2]

How do you normally run gnome-shell extensions in Cinnamon? there is currently no intended support for Cinnamon for this extension, AFAIK Cinnamon doesn't run gnome-shell / Gnome 40 or even mutter, and it doesn't look for extensions in the same place.

I suppose to answer your original question; No, currently this shouldn't work with Linux Mint Cinnamon without some refactoring or a compatibility tool.
If you have a way of running gnome extensions on cinnamon that normally works, then I would ask what method you're using and what steps you followed to install and maybe I can offer some suggestions.