Not OP, but you pretty much have to run the Celeron ones. I don't think the docker image would work with the Realtek ones (the ones that end in j). I have a DS220+ (J4025 with dual core only). It works ok, you pretty much max out one of the cores running a 4K stream. I would recommend separating the storage and server if you can afford it. The price difference between the quad core (4 bay) and 2 core (has 2 bay) is enough to get a 2 bay + a N95 mini pc that can handle 4 streams of 4K.
Another idea is to get a thin client with an i7 or i9 (you probably want at least 10th gen at this point) and either an external enclosure for a few SSDs or if you find one with a PCIE slot, a PCIE card to fit maybe 4x m.2 SSDs. Some good deals are out there on U.2 SSDs if you look as well, like 8TB for $400 from Intel or WD good.
Don’t forget that Asrock Rack and Supermicro sell Atom and Xeon-D boards, as well as some Ryzen AM4/5 models if you want to DIY. There are great cases out there (eg Fractal Node 304/804) these days that support full-size modular PSUs with 80+ Titanium ratings to sip power. That’s been my biggest gripe with x86 over ARM: idle power usage for something I expect to have on 24x7 with PG&Es 50c/kWh. I just rebuilt my old desktop 5950x into a NAS using a Silverstone RM44 with air cooling, but it’s made to support liquid as well. That’s got plenty of room to fit 4X full-size GPUs and a power supply to match if you dabble with AI on the side. RTX 4060s are coming soon for $300 and that should be more than enough power for transcodes for the whole family.
I actually think buying a first gen Mac Mini M1 is a better idea with a thunderbolt drive storage. I have friends in California that does this for the reasons you mentioned. The utility price has made homelab servers and 3D printing pretty much non viable unless you want to pay a $300+ electricity bill.
He runs Jellyfin straight up from the downloads page [1]. I'm not entirely sure if it runs on Rosetta but he hasn't had any issues with multiple streams. For storage you have a couple options but enabling file sharing on macos + a large drive of your choice is your best bet.
If anyone wants to try this, be wary of transcode acceleration / HW passthru with Docker, esp on M1/M2. In general I’d love it if there was a GUI-less stripped-down MacOS Server edition instead of running the full-fat consumer OS as an always-on server.