Shortened URL's:
ProBox 4-bay: https://www.amazon.com/dp/B09WPPJHSS
ProBox 8-bay: https://www.amazon.com/dp/B09V3TGDFW
Yottamaster 4 bya: https://www.amazon.com/dp/B06XKWNJSB
One man's review: I have two of the ProBox 4-bay devices. While they were great for a while, both ended up somehow with greatly diminished performance and connectivity issues. Confirmed between two different PC's, multiple USB ports (including a PCIe USB card). Connecting HDD's directly to SATA didn't result in any performance degradation or connectivity problems.
Multi-bay USB3 enclosures are shite. I trust the Mediasonic 4-bay non-raid over eSATA, and there's also a 5-bay that I've got going with a SAS IT-mode HBA that's been doing fine so far.
https://www.amazon.com/dp/B09WPPJHSS
https://www.ebay.com/itm/404020493983
All you need is an inexpensive SAS HBA off ebay, 2x SAS cables, a 5-bay enclosure and a 5-bay rack (plus fan to cool the HBA) and a standard PC power supply, and you can support up to 8-10 drives outside the PC case with a fair minimum of fuss. Proof is my homelab :)
Connect everything to a UPS of course.
Your best bet would be to just use a JBOD enclosure. You can get either this one with 3.0 USB or if your mini-PC supports it, this one with USB 3.1 Gen 2.
Having a separate enclosure, while not ideal, should be fine. A lot of people run their OMV deployments using a pi connected to the USB header. Also, since the drives will be installed in the JBOD, you wouldn't have to worry about supplying power from the mini-PC as the JBOD will have it's own separate power source.