Search screen misses empty state result and search filters

### Your use case

#### What would you like to do?
As a user, I'd like to find rooms and content easily.

#### Why would you like to do it?
Search helps me to find rooms and content quickly.

#### How would you like to achieve it?
Use the search function in a familiar way how I learnt it from WhatsApp or Signal.

EXA shows just a blank screen:


WhatsApp (and similar Signal) shows the current room list as empty search state:


WhatsApp on top offers a few search filters, but that requires content search as well.

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

### Are you willing to provide a PR?

No

The issue names no files, tests, or client entry point. Start by locating the relevant Element client search screen and reviewing how empty results are rendered; determine the scope for an empty state and search filters. Done should include an agreed design and working search behavior matching the requested room, content, and filter states.

Written by the indexing model from the issue text.