JMAP does solve the same problems, and then some -- looking at the specs, it's more of a 1:1 mapping between IMAP+SMTP. I'd say that if you're looking at implementing _all the functionality of a modern email client_ you might want to look at that. If your use-case is just wanting to fetch emails from a bunch of inbox folders in real-time, potentially with some querying/filtering, I'd say JMAP is a bit overwhelming. Sure, it has some clients/libraries available, but only a few.

imapapi, in my opinion, being a RESTful API, appears to have a much simpler surface, seems easier to play with using curl, and if you're developing a bunch of RESTful services that use Swagger, it fits better with your stuff. So, less dev-time to use :-)