Update Plex via websockets (#28158)

* Save client identifier from auth for future use

* Use websocket events to update Plex

* Handle websocket disconnections

* Use aiohttp, shut down socket cleanly

* Bad rebase fix

* Don't connect websocket during config_flow validation, fix tests

* Move websocket handling to external library

* Close websocket session on HA stop

* Use external library, revert unnecessary test change

* Async & lint fixes

* Clean up websocket stopper on entry unload

* Setup websocket in component, pass actual needed object to library