> Users expect to be able to search their whole archive, so either you need all the data in the client, or the server needs to have access to the data... ...JMAP is therefore not introducing any new measures to address end-to-end encryption
You don't need to transfer gigs of emails to a client and manually search character-by-character through a massive trove of data. That isn't how search functions.
You can use probabilistic filters (like bloomfilters) so a client can actually run a search on thousands of emails using only a few hundred kilobytes (or maybe megabytes) of actual encrypted data. Basically, less than a modern webpage.
Each time a new email is downloaded, parse it, add it to an index segment, encrypt it, and store it back on the email server. Different clients can reuse the same indexes.