None of that matters if small footprint is the ultimate goal... RPi also consumes way less power than an x86-64 setup. I'm sure OP can look at prices and decide what's best for them.
So, rather than accept you made a likely well intentioned, but frankly horrible suggestion, you now want me to ignore the reality to make you feel better?!
1) Op didn't ask for the smallest possible solution, you just decided that if they did, your suggestion may not be so horrible.
2) RPi5 is a 10-13w media server, a Elitedesk G4 is 6-12w when doing hardware transcoding, includes iGPU, a multi-core x64 CPU, RAM and NVMe, along with HDD expansion options.
A new RPi5 4GB starter kit is £160, 8Gb is £220+, 16GB is £345+ and comes with a 32GB SD card, compare that to a Elitedesk G4 mini with a 6c/6t 8500T, 8-16GB and 256-512GB NVMe for anything from £75-125 and likely includes a windows licence, given the massive difference in price/spec and the power usage being the opposite of what you claimed, that only leaves size, and both are easily mounted on/behind a screen, one just has much, much better expansion options.
Honestly, I get you don't want to acknowledge you are wrong, but unless you already have a Rpi, no reasonable or sane person would buy a new one to do this job, it's a really, really poor fit.