When I use DHCP network settings, I get only the DNS server from DHCP (option 6), but neither the DNS domain (option 15) nor the more modern "search list" (option 119). I have not been able to get this via DHVPv4 nor DHCPv6.
When I look at /etc/resolv.conf, there is only a "." in the search entry. When I use standard debian 11.6, these options are honored.
Also, when I try to use the search list from the GUI, it works only when I specify the DNS server, too.
This is a problem when the NAS shall execute scripts with local hostnames in it - you must always specify the (default) domain.