So, the question is does this work? I don't think core wallet even allows to send to 0x addresses. Should I just say give me an actual BTC address?
You are lucky since the address format is invalid for bitcoin so you can't waste any coins accidentally.
But also even if it were the same, you still wouldn't be able to send bitcoin to another chain since the BBTC is a token on another chain and the only possible way is to sell your bitcoin first and buy that shittoken then send that instead.