Google's own Gemma models are runnable locally on a Pixel 9 Max so some lev of AI is replicatable client side. As far as Gmail running locally, it wouldn't be impossible for Gmail to be locally hosted and hit a local cache which syncs with a server only periodically over IMAP/JMAP/whatever if Google actually wanted to do it.

Right. But does it matter whether computation happens on the client or server? Probabaly on both in the end.

But yes I am looking forward to having my own LMS on my PC which only I have access to.