Not sure about jellyfin, but I assume it uses ffmpeg? The M1 is fast enough that ffmpeg can re-encode raw video footage from a high end camera (talking file sizes in the 10s of gigabyte range) an order of magnitude faster than realtime.
That would be about 20W. Apparently it uses 5W while idle — which is low compared to an Intel CPU but actually surprisingly high.
Power consumption on my M1 laptop averages at about 2.5 watts with active use based on the battery size and how long it lasts on a charge and that includes the screen. Apple hasn't optimised the Mac Mini for energy efficiency (though it is naturally pretty efficient).
TLDR if you really want the most energy efficient Mac, get a secondhand M1 MacBook Air. Or even better, consider an iPhone with Linux in a virtual machine - https://getutm.app/ - though I'm not sure how optimsied ffmpeg will be in that environment... the processor is certainly capable of encoding video quickly, it's a camera so it has to be able to encode video well.