Support BYOK with the built-in WebSocket connection adapter

[Visualizeit]

TanStack AI recently added BYOK support, where useChat forwards the
selected provider key through x-byok-* headers.

This works with the built-in fetch/XHR connection adapters, but does
not appear to work with the built-in WebSocket adapter because browser
WebSocket connections cannot attach arbitrary request headers.

It would be useful if BYOK were transport-agnostic at the useChat level,
with the WebSocket adapter forwarding the credential through a
standard application-level frame/protocol instead of requiring every
application to implement its own BYOK-over-WebSocket protocol.

[AlemTuzlak]

cc @tombeckenham

[tombeckenham]

Yeah I know. I looked, but you can't pass the key on the header in the same way with websockets.