The main goal here is to ensure the connection is built each connection
attempt. Previously, the access token would never be updated, leading to
outdated tokens failing repeatedly (in the connection retry loop) and
never being able to establish a new connection as a result.
Due to threading considerations, this isn't as simple as I would hope it
to be. I'm open to proposals as to a better way of handling this.
Also, keep in mind that this logic will need to be abstracted and
(re)used in `SpectatorClient` as well. I've intentionally not done that
yet until we agree that this is a good direction forward.
