There are a lot of atom or mobile i3/i5 powered mini PCs that actually are powered with a 12v brick, in fact most of the industrial ones are. Small form factor, passive cooling, can play media for you and usually comes with 4x 1/2.5gbit Ethernet, so it can double as a router/switch. Usually 10-15w power draw.
Go to AliExpress and simply search for minipc and make sure it has a SATA connector for your hard drive.
Something more like this https://a.co/d/0bgPCSvQ - it should use half the power, it’s way smaller, 2x SATA if you want 2 drives. I haven’t checked if this specific one is 12V, but there are dozens in the same form factor and with similar specs.