To close the loop on this, the 10gbps FlexIO module 56Q71AA works fine in an HP EliteDesk Mini G6 (10700T 35W model). I was also wondering whether it would work and I couldn't find anything definitive online so I bit the bullet and bought one in the hopes that it would work. It was an easy fit as one would expect. It came with extra long screws as it has a heatsink that the screws need to reach through. I'm getting full 10gbps speeds and the cooling system in the unit seems to handle whatever extra heat load there is without spinning up the fans more than with the USB module that this replaced. I run Proxmox (7.4) on that box and the adapter was recognized without any fuss. The 2.5gbps module is clearly the better value (~$25) but if you need/want 10gbps and are willing to spend the extra (the one I found was ~$135) then I can recommend it for a G6.