Particularly in low-load scenarios there can be quite a big difference when it comes to PSU efficiency. While newer ATX PSUs have become better with regards to efficiency at low load, a Pico PSU can still be quite a bit better. Older ATX PSU often don't even reach 60 % efficiency at 5 % load (which would be a typical load for such a system at idle), sometimes considerably less than that. At the same load a Pico PSU can easily be at 85 % efficiency.
Of course, at higher loads the difference is way smaller.
Since none of these require a Raspberry Pi to run, I would suggest using a mini PC (with an Intel N100 or similar) instead of a Pi 5. With all the accessories needed for the Pi, a mini PC can actually be cheaper and of course a lot more powerful. Since the Pi 5 is very power-inefficient, a mini PC can even be better in that regard too if that matters to you.
Especially for Jellyfin a PC with an Intel CPU with integrated GPU is awesome, since Jellyfin supports hardware transcoding with that.