Jumpy "Send to" screen

### Your use case

Almost every time I share a file and arrive at the “Send to” screen, the list of rooms reorders itself without any clear indication of why.
And when a room is selected for sharing, the layout-change is jarring.
#### What would you like to do?
- Sort with a predictable order e.g. last messaged or rooms you're most active in.
- - Do not reorder list once opened.
- Use a bottom overlay instead of changing the layout.
- - **Consider also:**
- - Moving the send button to appear in the bottom overlay.
- - Replace the search bar with a search button on the top right. Or Putting a filter on the top right.
#### Why would you like to do it?
The current behaviour creates unnecessary cognitive load and interaction friction. When the list reorders itself, users have to re-scan it. And the layout change after selecting a room is unexpected.

### Have you considered any alternatives?

Show list only after it's loaded and do not reorder once shown.

### Additional context

_No response_

### Are you willing to provide a PR?

No

The issue names only the Android “Send to” screen and no files or tests. Start by locating that screen and observing room ordering and the selected-room layout; done means a predictable, stable list and a non-jarring selection presentation after one design direction is chosen.

Written by the indexing model from the issue text.