Find a way to compose common implementation of the `RoomViewControllerDelegate` between `RoomCoordinator` and `ExploreRoomCoordinator`

### Your use case

`RoomCoordinator` and `ExploreRoomCoordinator` are both `RoomViewControllerDelegate` with a large amount of common code. The idea would be to extract common code into independent modules that could be used by both coordinators.

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

Start by comparing the RoomCoordinator and ExploreRoomCoordinator implementations of RoomViewControllerDelegate to identify their shared responsibilities. Confirm the intended module boundaries with maintainers; done means both coordinators use independently reusable common code without changing their existing behavior.

Written by the indexing model from the issue text.