since it's a windows based program (and it's impossible to find a raspberry pi for a decent price in 2022, and trying to get a windows program running in linux is never straightforward), I would go with a windows PC, and my recommend is one of these refurbished dell small form PCs. I don't know much about projectors so I just picked the one amazon recommended.

https://www.amazon.com/Dell-OptiPlex-i5-7600T-Windows-Renewed/dp/B07XLF99BY

https://www.amazon.com/Projector-Video-Projector-Multimedia-Compatible-Smartphone/dp/B07MTCMHZX