Any IMAP over REST API should just implement JMAP (RFC 8620 and 8621).

Indeed. Which is the perfect occasion to ask: who besides Fastmail implements it ?

Right now - not heaps.

https://jmap.io/software.html has a list of some known implementations.

https://github.com/jmapio/jmap-perl seems the most similar to the project discussed here. Anyone have experience with it?