[3.0.5 Backport] Update websocket implementation

The websocket implementation uses the old /x/net/websocket library, which is lacking features we'd like (such as automatic ping/pong and being able to do a close handshake).

Potential alternatives:

• https://github.com/nhooyr/websocket
• https://github.com/gorilla/websocket (more popular but semi-unmaintained and lacking some features like close handshakes)

Also evaluate effect on performance in the e2e/BLIP tests.