Late to this, but the "low power" half of the ask never got answered with actual numbers, and that is exactly where 8-core AMD mini PCs trip people up, so here are measured idle figures for the boxes in play.
Idle on these tracks the AMD generation, not the core count, and it swings about 5x:
Beelink SER5 Pro (Ryzen 7 5800H, 8C/16T): ~5.3-8.2 W idle, takes 64 GB DDR4. Andrew's pick is genuinely one of the lowest-idle 8-core boxes going, so it is a good steer for your priority.
Aoostar R7 (Ryzen 7 5700U, 8C): ~7.3 W idle, but 32 GB max.
Minisforum UM690 (Ryzen 9 6900HX, 8C): ~8-10 W idle, 64 GB.
Beelink SER8 (Ryzen 7 8845HS, 8C): ~7-10 W idle (package 3.5-4.7 W) if you want a newer chip.
The catch: newer is not lower here. A SER6 Pro (7735HS) measures 20-35 W idle and a UM790 Pro (7940HS) 25-45 W, so reaching for the latest Zen4 HS chip can triple your standby draw versus the 5800H. On an always-on box at UK rates (~£2-2.50 per watt per year) that gap is most of your running cost.
On the EliteDesk 805 G8 idea, nothing wrong with a validated big-name box, just note the AMD Pro mini line tends to ship Realtek 1GbE NICs (the 705 G4 and Lenovo M75q both do), which are fine under Proxmox/Debian but not under ESXi if that ever matters. I do not have a clean measured idle number for the 805 G8 specifically, so I will not invent one.
On dropping your existing Proxmox SSD straight into new hardware: it usually boots since it is just Debian, but two things bite. The NIC comes up under a different name on the new board, so vmbr0 loses its uplink until you fix /etc/network/interfaces. And you are on Legacy BIOS now, so a UEFI-only box means repairing the bootloader. Doable, just not always plug-and-play, so pringlestuffs' caution is fair.
One extra if you ever want iGPU passthrough for transcoding: the Ryzen APUs (680M/780M) hit the AMD reset bug where the GPU only resets once per host power-on. The older 5800H Vega is less affected than the 680M. Ignore this if passthrough is not in the plan.
Full disclosure, I built a small free thing for exactly this decision because I got tired of re-deriving measured idle / NIC chipset / passthrough notes per box from scattered reviews: https://idlewatt.vercel.app (every figure cited to a wall-meter source, data is CC-BY at https://github.com/SolvoHQ/homelab-mini-pc-dataset). Corrections welcome if your SER5 idles differently from what is listed.