I don't know an answer to your question (although I would doubt there are monitors with airplay built in as apple has a close hold on who can airplay, and TVs have only just got it this last year).
Your options are for a TV that can airplay, which is not necessarily the best for gaming on, or software based approaches to stream too, during my lockdown lessons I have used airplay server to airplay my ipad to my monitor within windows, and then stream to the students through Teams. This could also work for you!