Add state generic to WebSocket

[lucasgranberg]

Summary

Add generic state to websockets just like for requests
#3131

Checklist

• I understand that this PR may be closed in case there was no previous discussion. (This doesn't apply to typos!)
• I've added a test for each change that was introduced, and I tried as much as possible to make a single atomic change.
• I've updated the documentation accordingly.