* Improve Home Assistant Core WebSocket proxy implementation
This change removes unnecessary task creation for every WebSocket
message and instead creates just two tasks, one for each direction.
This improves performance by about factor of 3 when measuring 1000
WebSocket requests to Core (from ~530ms to ~160ms).
While at it, also handle all WebSocket message related to closing the
WebSocket and report all other errors as warnings instead of just info.
* Improve logging and error handling
* Add WS client error test case
* Use asyncio.gather directly
* Use asyncio.wait to handle exceptions gracefully
* Drop cancellation handling and correctly wait for the other proxy task
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