Internet Connection Sharing started causing intermittent disconnections recently

I have had an up to date Windows 11 custom PC with 2 active network cards (1Gb and 10Gb) for a few months. I started noticing a few weeks some strange but rare disconnections, like some Remote Desktop connections (on alocal network) that dropped overnight. I didn't make much of it until a few days ago when they were more and more frequent to the point that today I can't have any Remote Desktop connection to any machine stable for more than a few minutes. When this occurs my browsers now hang (and Firefox even has to be killed and restarted). Windows does not notice any problem with the network, and the strange thing is that I can still ping any machine out there (local or web)...
After a lot of try and error I made sure that the problem was localized to this computer. I even pinpointed it to the activation of the Internet Connection Sharing on the 10Gb card: the trouble occur as soon as it is active. Nothing happens when it is inactive.

I have used the same kind of setup for many years now without trouble, starting with Windows 10: I connect my Hyper-V VMs to an internal network adapter so that they have an internal IP address (and DHCP), and I share Internet access with ICS (via the 10Gb network card). And now this makes my computer unusable...

Any ideas?