Xeno
Nothing to add except calling the PSP retro made me feel old.
I’ve had similar requirements for a few years. Finally settled on 8 bay synology with a dell micro optiplex. I have a 10gb card in the synology and actually use a usb to 2.5gbE in the dell with zero stability issues. Some synology products can transcode a stream or two of 4k with quick sync but not many of the 8 bay ones. I have a 9th gen i5 with 32gb of ram that handles all my transcoding needs. Done 2x 4k transcodes with no issues while also streaming other 1080p for additional users.
I believe it is a micro 3070. Amazon link just for example, but very easy to find under $250 and very low power consumption. https://www.amazon.com/Dell-OptiPlex-3070-Desktop-Computer/dp/B07TTCJB2P?th=1
I actually worked on the team that designed these! If I recall correctly, the top connector is for the motherboard BMC. It should work fine without being connected. The right hand side as others said is power.