In #3665 I made it so that the initial startup for the kernel uses the same timeout as our restart logic. I believe this is because the websocket times out.

For some reason, I have no issues with this when working with this locally, only remotely.

There is a simple fix for this, by making the timeout change only apply to the restart (which does work on its own). However, the real problem has to do with the fact that the websocket handshake can be achieved via some other means, rather than tied to the activity of the kernel. Fixing that so that we can have better visibility on the state of the kernel (independent on the success of the handshake, since that isn't strictly needed or the current timeout mechanism would stop slow kernels from ever starting).