Correcting some misconceptions...
Element for Android doesn’t support searching in encrypted channels
That's true of regular Element for Android, but it's being replaced with Element X (which is built with Rust). I would expect search to be added there if it isn't already.
and I think you can’t use E2EE in the browser at all(?)
I have done it in Firefox, so that's false. Perhaps you had trouble with a specific browser?
plus basically every other client has even more drawbacks when it comes to E2EE.
Nheko handles E2EE just fine, so that would seem to be false as well.
Since you're looking for recommendations, it would help if you said which clients you tried and what problems you had with them.
In case you haven't seen it, you can set a Features: E2EE filter on this list:
https://matrix.org/ecosystem/clients/
Amen.
Spoiler alert: Few of them are good, and those few are so simple that you might as well not use a library.
The only way to correctly validate an email address is to send a message to it, and verify that it arrived.