What did you setup for the PIVD on the ports? Did you enable any trunking?
For what you are try to setup from your diagram, you would be better off make port 5 a separate network and get rid of the vlans and running 2 lan networks.
The way you have it set now is the not correct for vlan...
Have used this type of box before, 4 to 18 ports.
https://www.amazon.com/ARES-CCTV-Power-Supply-PORT/dp/B07BN4HLZN/ref=sr_1_4?dchild=1&keywords=12%2Bvolt%2Bpower%2Bsupply%2Bbox&qid=1602083515&s=electronics&sr=1-4&th=1
Sound like the SFF will be the best for your needs. Most of the HP from G3 or G4 will have M.2 Slot. Just make sure you check what type drive your M.2 slot supports PciE, Sata or NVMe.
The NUC and Mini / micro are the same platform design. You ask what the smallest size you could use for BI with 4 cams. I have 8 setup mini’s running 2-4 cams over 2+ years on mini. These systems are in a Kiosk stand and could not fit a small form factor PC. If I could have fit SFF I would have...
HP Mini 400 or 600, dell micro PC 3050 3060. Get unit with M.2 for main os and on slot open for 2.5" drive. You can get new or refurbished in both units.