While looking over this document for other BenQ projectors I saw that some support PJLink. A quick DuckDuckGo search to find out what PJLink is lead me to discover there’s already an integration! I turned on the network standby on my projector, configured the integration in YAML, restarted my home assistant, and the new entity popped up and bingo! I can turn it on/off and change the input! That’s all I really need 