Workaround instead of solution:
You could buy a Wireless HDMI Transmitter and Receiver setup. Should be able to find a version where it kinda looks like a Compute Stick (HDMI end) that is powered with a USB cable.
This isn't much easier than using an HDMI cable and unless you have use for it at home afterwards it is a costly solution:
https://duckduckgo.com/?q=Wireless+HDMI+Transmitter+and+Receiver
edit: cleaned up duckgogo link
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Your link doesn't work, but I still found what you mean. I think at that point I'd probably look into the Microsoft Wireless Display Adapter or something similar instead, as Miracast on Linux actually works quite well with GNOME Network Displays. But my current goal is not having to connect any additional hardware to the projector, so I will be looking into pyatv for now.
I guess your "best" solution is to talk to Campus IT and sell them on the idea of buying the Microsoft Wireless Display Adapters and use as a secondary solutions with all projectors/tvs. Then all you have to do is plug in the client end that's already there waiting for you. ;-)
My main experience casting to Apple TVs from Linux is with Home Assistant, which has a few different addons related to Apple TV. Unfortunately most are related to receiving casts or casting music, and it doesn’t look like any support screen mirroring. The main library - https://pyatv.dev - has only limited support for AirPlay, and its documentation indicates it lacks screen mirroring support. If you just want to stream a video, though, then it would be worth looking into.
open-airplay with the auth solution by @funtax (on Github) is the approach I would try, but unfortunately I can’t comment as to whether or not that actually still works.
I can't find any "funtax" user in the linked openairplay repo, but it appears that I have completely missed pyatv's ability to stream video. As long as it can stream video I think I can make it do screen mirroring too. Thank you very much, I will be looking into pyatv now!
I don’t think they contributed to openairplay, but they mentioned in an open issue in the openairplay repo that they had created a separate repo to handle the auth piece. Strangely I can’t find the issue now, but this is the repo I was talking about for that: https://github.com/openairplay/AirPlayAuth
That all said, it pyatv will work for you it looks like a much better bet, anyway. Good luck!