Encrypted room search should also Just Work... but only on Element Desktop (which uses tantivy to do clientside search). We are in the process of porting this to Element X (and Element Web), but after an initial spike over the summer we're waiting for either funding or manpower to finish it.
I'm using Element X and there seems to be no search button for messages at all.
So I cannot even search for "shopping" to find the shopping list, or "address" to find the address a friend sent me some days ago.
It is simple to see why the normal user will have a bad everyday experience.
The app uses 160 MB user data on my phone which fits a lot of text, why cannot I just search it?
https://github.com/pkulak/matui/releases/tag/v0.6.0
For encrypted rooms it just starts pulling messages down and looking for substrings... but it's actually works pretty well if you don't want to search back to the beginning of time.
matui looks super fun - you should come tell https://matrix.to/#/#twim:matrix.org about it :)