I’m using it to connect my personal Windows laptop to our corporate office, so was wanting easier access to local servers where we just specify the server name rather than the FQDN. I did eventually find an answer, so here it is in case it helps someone else:
In Registry editor, navigate to
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Tcpip\Parameters
Add a string value named SearchList with a comma-separated list of domains.
Note that this isn’t connection-specific, it’s global. In my case, I’m OK with that. From the GitHub source, it looks like “DNSSearch” will be a config option eventually for the wireguard Windows client and that will be a better solution than making it global for most people.