I found the problem.
I am using OPNsense and forgot to disable TX checksum offloading. Very interesting that this checksum offloading caused catastrophic network disruptions on a Realtek nic, but no noticeable performance hit on Intel nics. This was an old host that featured a Realtek card. All my recent hosts that I use have only Intel nics. That is why I forgot about the whole offloading thing.
Thanks for the tips.
Best wishes to the whole community!