Laptop CPUs are, however, really well optimised for very low consumption when idling and that's what you should be using for a mediacenter.
Also, IMHO, ASRock Deskmini would not be a good idea for a media center since it's using desktop CPUs. The idle power draw will not be as good as mini pc with a laptop CPU.
My desktop server uses 50W at idle. ASRock Z390 motherboard, Pentium G5400, 32GB RAM, no GPU. There are 15HDDs, but 50W is with all of them spun down. It hits 120W will all disks spun up and CPU under load. I've come to the conclusion it's the motherboard, because the parts individually shouldn't draw that much power.
On the other hand, if you can, please consider using a more energy efficient alternative (and/or ensure you're getting the electricity from green sources) - the planet will warm up regardless of whether the electricity was cheap or expensive.
My total household usage averages around 4.5KWh/day so adding that 45W 24/7 server would add about 24% to overall load! It would need to be an important little server to justify the increase.