Would be interesting to see it, did you publish it yet?
Only the client parts. And only the client parts its actually using. JMAP is designed to make clients much simpler than servers. A JMAP server needs to actually parse message envelopes - which is way more difficult to do correctly than people think. A JMAP client can just ask the server for pre-parsed messages.
The code is here:
https://github.com/josephg/claude-mail
Claude put its JMAP API wrapper in a child crate (confusingly also called jmap-client).