Just went through an upgrade of my TV pc recently.
HP 800 G4 mini i5-8500T 16GB 256GB nvme about NZ$220 inc. post from Amazon.
Went with 8th gen cpu for win11 compatibility. It has 2 nvme slots (and a 2.5 sata) so I chucked a 2nd cheapie 2TB nvme in for the Jellyfin server.
The HDMI module is optional on these so I made sure this one had it. It is also HDMI v2 so can do 4k/HDR (some units around this age are only HDMI v1.4)