It’s a newer development, GPS proper doesn’t support signing. Galileo is a different satellite.

It takes about 5 minutes to transmit a signature, as I understand? The receiver then can try to find the combination of navigation packets that gives the right signature, and recover its position this way.

So yeah, this should solve the spoofing issues for most cases. Low-orbit sats would be able to transmit a signature every millisecond or so, but that's not really necessary.