It depends on your provider, unfortunately. If you use their iCloud mail service, search works fine – it appears to have some way to do server-side search for their own email.
I'm also close to a much more releasable version of the proxy which was first written back in 2014: https://github.com/jmapio/jmap-perl/ -- which can wrap existing IMAP/CalDAV/CardDAV/Submission infrastructure so you can access it via JMAP.