Airplay to ceiling-mounted projector

I have a ceiling-mounted projector and I would like to stream from my Mac to it using Airplay.

Currently I see two solutions:

• get an Apple TV, put it up there and just use it to stream with Airplay 2 --> $149 + an additional remote
• get a Chromecast and use the function in specific apps (e.g. Netflix) --> $35

There seem to be an effort to provide Miracast / Airplay dongles but they seem to be struggling with any copyrighted content (e.g. Disney+).

Also, my particular projector has internal space for a usb-powered HDMI-dongle, where the Chromecast could fit, but not an Apple TV.

Does anyone has experience doing this, and which option would you recommend ? Please consider that the projector is ceiling-mounted, which impacts cabling.

I wish Apple had a $50 Airplay dongle to sell...