client-api: Send WebSocket messages fragmented

[kim]

RFC 6455, Section 5.4 describes message fragmentation, and we can do that with tungstenite.

It does seem to help getting control messages (ping, pong, close) through without head-of-line blocking.

Expected complexity level and risk

2 - Need to test with clients

Testing

TBD - some more abstraction is needed due to the difficulty of synthetically producing a large outgoing message.