I’ve moved most active and new accounts over to Proton, and I’d like to migrate all my old emails too, but before that I’ll need to be able to search mail content from mobile.
Building a local encrypted index of the contents of the email is probably what's taking them time to build. Remember encryption. Can't be done server side.
They describe the solution in the link I provided for the desktop functionality for this; it should be fairly similar on iOS except for the limitations to background jobs.
Not a dev but it could be quite different than fairly similar. The encrypted search makes use of the browser storage. This isn‘t even working on iOS due to limitations.
EDIT: Just checked my wife's phone and there is a search icon in the top right on iOS latest update...works great even for content. Are you running an older version?
I'm amazed the iOS version doesn't have a search function. That should be at the top of the list, they already have it for android.