Phantom typing notifications

### Steps to reproduce

1. View a room for the first time in a while
2. If a user was typing the last time you viewed it, you still see a typing notif for them - even if they stopped typing hours ago.
3. Eventually that typing notif times out.

### Outcome

#### What did you expect?

Reliable typing notifs

#### What happened instead?

Phantom typing notifs.

### Operating system

_No response_

### Browser information

_No response_

### URL for webapp

_No response_

### Application version

Element Nightly version: 2024022801 Crypto version: Rust SDK 0.7.0 (b1918e9), Vodozemac 0.5.1

### Homeserver

matrix.org

### Will you send logs?

Yes

Reproduce the issue by opening a room in Element Nightly after a long absence, using matrix.org if available, and observe whether a previous typing notification remains. Trace the typing-notification lifecycle from the reproduction steps, then verify that stopped typing activity is not shown when returning to the room and that current typing notifications still work.

Written by the indexing model from the issue text.