None. Microsoft has Copilot in preview mode in Windows and it's not very integrated apart from a chat window. I doubt GNOME/KDE will be able to dedicate enough resources to adding an assistant that is well integrated with the desktop environment any time soon.
A search in Fedora yields a single GSoC project[0] limited in scope to NetworkManager and it's not clear if anyone actually is working on that.
If the use case you're interested in is actually having the LLM doing things for you in SaaS applications, that wouldn't need deep integration but, considering Google is yet to deliver a Google Drive client for Linux, I wouldn't hold my breath waiting for a native Linux AI-assisted assistant.
Your best option right now is to interface with the assistants through their web interface and hope they have plugins/extensions to interact with things you want.
Other than that, some people have built prototypes running LLMs locally that talk to things like Home Assistant. But again, no deep desktop integration.
0 - https://docs.fedoraproject.org/en-US/mentored-projects/gsoc/...