Projector suggestions

I'm trying to find a new projector for my home theater. I don't need high end, but it should be at least 1080p (i.e., 4K isnt necessary). I mention that because of my budget: I'm looking for something around $500, but I might be able to go up to $1000. The other main requirement is that I'm able to turn it on/off via Home Assistant.

Other nice features to have, but nott requirements:

• Ability to adjust vertical and horizontal keystones (I mount this projector on a ceiling)
• Decent brightness & contract (it doesn't have to be the brightest on the market, but it shouldn't be the dimmest)
• HDMI connector (I have a 50 foot HDMI cable now, but if sending data to projectors via wifi is a thing, that would be better)

Thansk for your suggestions.