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.
