You can specify the order in a file in /etc/systemd/network/<nic>.network
The following is from memory - perhaps my memory is not as good as I hope - I will verify it.
[Network]
DNS=192.168.1.0
Domains=mynet.lan
This should ensure that all hostnames on mynet.lan is resolved using the local dns.
Just checked with the Arch Wiki.
A better approach seems to be to edit /etc/systemd/resolved.conf.d/dns_servers.conf
https://wiki.archlinux.org/title/Systemd-resolved#Manually
Example
[Resolve]
DNS=192.168.1.1#local-dns ip.x.y.z#isp-dns
Domains=mynet.local
Also see the troubleshooting section