Most of the data inside `RoomInfo` is not available from its API

`BaseRoom::subscribe_info` allows to keep track of changes in the `RoomInfo`. However most of the data in `RoomInfo` is not accessible from its methods but from the methods of `BaseRoom`. That makes receiving the `RoomInfo` from the subscriber not that interesting.

I would like to find a way to have all the `RoomInfo`-related methods on `RoomInfo`, while having a simple way to access them on `Room`. The issue I see is that always using `BaseRoom::clone_info` means we need to clone the whole structure when we might want to use a single field.

Here is what we can't do:
1. Redefining every method on `Room` manually is annoying, and needs to be kept up to date.
2. We can't implement `Deref` because that allows the user to keep a reference to the `RoomInfo`, but it is mutable.

Maybe cloning the `RoomInfo` each time is actually a non-issue, given that it is already what happens with `BaseRoom::subscribe_info`.

Start by reading BaseRoom::subscribe_info, BaseRoom::clone_info, RoomInfo, and Room to understand which methods and data are currently exposed. Compare the existing subscriber and cloning behavior, then define a consistent API design that makes RoomInfo data accessible while keeping Room convenient to use. Done means the chosen approach covers the reported RoomInfo-related methods without exposing an invalid mutable reference.

Written by the indexing model from the issue text.