Hi,
NetworkManager pushes DNS server configuration (and associated bits like domain search and routing domains) over dbus to resolved. That way it "[tells resolved how to] split DNS according to routing". Of course, after the name has been resolved to an IP address, the packets to that IP address are routed too. So there is "routing" in the sense of deciding which interface is appropriate for a given DNS name and "routing" in the sense of deciding which interface is appropriate for a given IP address.
This explain how this issue came in the first place. https://gnuguix-drive.mycozy.cloud/public?sharecode=YvERPGX14g5S
Cheers, Cuckoo's Calling.