Duplication problem when adding an existing room

### Steps to reproduce

When adding an existing room to a space, we've noticed that conversations with individual people now lists their display name twice in the list of conversations.

For example, if I had a conversation with "John D" in the "Marketing" room of the "Corporate" space and then added that room to a new space (i.e., "Marketing Division"), my conversations with "John D" now show "John D and John D" as the display name in the list of conversations.

This bug is limited to iOS. Android users and desktop users are not seeing the same issue.

### Outcome

I expect the Display Name value to not be duplicated.

### Your phone model

iPhone 15 Pro

### Operating system version

iOS 17.4.1

### Application version

1.11.9

### Homeserver

Synapse 1.93.0

### Will you send logs?

No