The DHCP server allows setting a vendor-specific option for Ubiquiti Unifi Network Controllers:

set service dhcp-server shared-network-name MANAGEMENT option vendor-option ubiquiti unifi-controller 1.2.3.4

It should use DHCP Option 43. However, I believe there’s a small bug in the underlying config where it’s using Option 1 instead.

See this line: /data/templates/dhcp-server/kea-dhcp4.conf.j2

To verify this, modified the following:

/run/kea/kea-dhcp4.conf

by changing

{
    "name": "unifi-controller",
    "code": 1,
    "type": "ipv4-address",
    "space": "ubnt"
}

to

{
    "name": "unifi-controller",
    "code": 43,
    "type": "ipv4-address",
    "space": "ubnt"
}

And it seems to be working now.