Feature request: Add search functionality inside rooms (in-chat message search)

### Your use case

**Problem / Current behavior**
In Element X, there is no way to search for messages inside a room/chat.
Once you are inside a room, there is no search bar or option to find specific messages, keywords, or older conversations within that room.

**Expected behavior**
I would like to have a search feature inside each room that allows users to:

Search for keywords or phrases within that specific room
See results with timestamps and quick jump to the message
Filter results if possible (e.g. by sender, date, media, etc.)

This is a very common and useful feature in modern messaging apps (Telegram, WhatsApp, Discord, Slack, and even the old Element client had basic search).

**Why this matters**
Makes it much easier to find important messages in long or busy rooms
Especially helpful in group chats with hundreds or thousands of messages
Improves productivity and user experience significantly

**Steps to reproduce / Current limitation**
Open any room in Element X
Try to find a specific message or keyword from earlier
There is no search option available

**Additional context**
Global search (searching across all rooms) might already exist or not, but in-room search is missing.
Please consider adding a search icon at the top of the chat screen.

**Platform:**
Element X Android
Element X iOS

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

### Are you willing to provide a PR?

Yes

Start by locating the Element X Android room screen and checking whether global search already exists. Define the supported search scope, result presentation, filters, and quick-jump behavior before identifying the relevant implementation and tests; done means users can search messages within a room on the stated Android and iOS targets.

Written by the indexing model from the issue text.