From a cooling standpoint, you probably don’t want go any smaller than a Small Form Factor desktop. These are large enough to have a proper heatsink and fan on the cpu, enough space for a dedicated video card, have the motherboard connections for a card, large enough power supply, and can support a case fan.

Mini desktops have minimal cooling capacity, definitely no case fan.

For example, I run a Dell SFF (OptiPlex 7050) as a server for virtual machines, Jellyfin host, file server, and media converter. It’s an older machine with an 80 watt power supply, no case fan, and the stock cooler/fan is fortunately well designed.

That stock cooler also evacuates the case, but can’t move enough air to keep the large drive I installed at reasonable temps. Adding a case fan dropped the drive temps by more than 20F.

Without the sizeable cpu cooler and it’s fan, there’s no way to keep the cpu cool when doing anything more than basic desktop functions. A mini pc would quickly overheat.