The Join button does not disappear when the DM call is finished

### Steps to reproduce

1. Where are you starting? What can you see?
- I'm in a 1:1 call with Florian

2. What do you click?
- One of us hangs up and the call is ended (It's a DM call so it finishes automatically when one party leaves the call)

3. More steps…
- The join button remains in the header which is confusing and not the expected behaviour

### Outcome

#### What did you expect?
The buttons in the room header should be normal, there should not be a 'join button'

#### What happened instead?
There was a join button and it only cleared when i sent a message to the room

### Operating system

Mac

### Browser information

Element Nightly

### URL for webapp

_No response_

### Will you send logs?

Yes

Start by reproducing the 1:1 DM call in Element Nightly and inspect the room-header join-button state after one participant hangs up. Trace the call-ended update and verify that the join button disappears immediately, without requiring a message to be sent; the payload names no files or tests.

Written by the indexing model from the issue text.