Why wouldn't E2EE work in the browser versions of the clients? You just log in, verify from a logged in client, and then everything works. Decryption of message history can take a while, but it gets there eventually, and sending and receiving new messages should work with encryption, right away.
Search is tricky because the client essentially has to download, decrypt, then index, your entire user history. The server can't do the search for you, because it never sees your messages in cleartext.
Syphon does actually do this on mobile, but it's in alpha, and while it can do E2EE you have to export your keys from another client, then import them, to get it working. No easy emoji verification.
You might look at schildi, which is a fork of element with implementations for a a bunch of extra stuff. You'll have to get past the app icon, tho.