Move `Channel::channel_id` and some other methods to `ChannelContext` impl

Move `Channel::channel_id` and some other methods to `ChannelContext` impl

This is one of a series of commits to make sure methods are moved by
chunks so they are easily reviewable in diffs. Unfortunately they are
not purely move-only as fields need to be updated for things to
compile, but these should be quite clear.

This commit also uses the `context` field where needed for compilation
and tests to pass due to the above change.