Add an automatic "unread" section

### Your use case

#### What would you like to do?

Have a section that shows all rooms or people with unread messages.

#### Why would you like to do it?

To be able to easily find unread messages.

#### How would you like to achieve it?

See above.

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

The issue names no files, tests, or entry points. First clarify how the unread section should behave and which rooms or people it should include, then identify the relevant room-list entry point. Done means the web client automatically presents all intended unread conversations in a clearly usable section.

Written by the indexing model from the issue text.