I was able to test a Zigbee-only automation and that one keeps working if you unplug the Ethernet. That means the automation engine keeps running and I guess we can discard the possibility of the hub entering a panic mode where it disables features if the Ethernet is down.
So there’s indeed something weird about handling Thread devices directly connected to the hub’s Thread radio that fails when the not needed Ethernet link is down. The automation should work fine and seems like a bug. It may also be related to the Matter controller features and not Thread.