Allow room search to filter by mxid, room alias, etc

### Your use case

This is effectively the android counterpart to https://github.com/vector-im/element-web/issues/16253

#### What would you like to do?
I'm always frustrated when I try to find my smartass friend who uses a single unicode special character (♠) as display name in my people/room list, and they're not in the top 5 recent people I talked to. So this means I have to type an emoji and hope it's the right variant (\u2660 or \u2660\uFE0F) or scroll down for hours while scanning for the right room.
Sure, I could warn them about this and then stop messaging them unless they change their display name, but I think Element could simply handle such things better.

#### How would you like to achieve it?
Mirror the search/filter algorithm from Desktop "New Search Experience"

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

### Are you willing to provide a PR?

No