Create a connection with the web socket server after connecting to wifi and rebooting with load()

Yes, that makes sense, after load() allows you to use the websocket as you need rather than one-time.

I don't think you are that far away. At the moment your websocket code is sort of orphaned but if you've got logging statements that appear after load() has run and when you're connected on your network that's a great start.

Either bring your socket code into that part too, or maybe wrap the socket code in a function and just call it to set it up?

Briefly looking at the README for the Espruino Wifi Manager the callback function is used on successful connection, so that's probably were you have your logging that works(?) and where you need to put your code (either pasted or the function call). I'm guessing a bit.

If that does not help, post up your code as you have it now.