Closes https://github.com/ppy/osu/issues/26835.
I must have not re-tested this correctly after all the refactors...
Basically the issue is that the websocket connection would only come
online when the API state changed to full `Online`. In particular
the connector would not attempt to connect when the API state was
`RequiresSecondFactorAuth`, giving the link-based flow no chance to
actually work.
The change in `WebSocketNotificationsClientConnector` is relevant in
that queueing requests does nothing before the API state changes to full
`Online`. It also cleans up things a bit code-wise so... win?
And yes, this means that the _other_ `PersistentEndpointClientConnector`
implementations (i.e. SignalR connectors) will also come online earlier
after this. Based on previous discussions
(https://github.com/ppy/osu/pull/25480#discussion_r1395566545) I think
this is fine, but if it is _not_ fine, then it can be fixed by exposing
a virtual that lets a connector to decide when to come alive, I guess.
This is a prerequisite for https://github.com/ppy/osu/pull/25480.
The `WebSocketNotificationsClient` was tightly coupled to chat specifics
making it difficult to use in the second factor verification flow.
This commit's goal is to separate the websocket connection and message
handling concerns from specific chat logic concerns.
