Just wanted to update you with my current status. I decided to verify that I correctly followed Gary’s recommendations and sure enough I had done the opposite (of course I did). Since then I have seen no further unexpected dismounts if I don’t put the Mac to sleep. Also note, that I am not using PD power to the Mate mini as I don’t have anything connected pulling power from the hub.
For the fun of it I did put it to sleep and as expected, the Bee-Link SDD drive was eventually dismounted. This appears to be just the nature of using the Mate mini with the Mac mini. It isn’t ideal, but I can live with it.
Thanks again to Gary for pointing me in the right direction.