For linking activity back to your person? Without name, payment details, photos of face, or IRL social graph the easiest path that comes to mind is IP address. But that's going to involve additional inquiries and is likely ambiguous (unless you live alone, but determining that is again more work).
“allow google to search for devices on your network?”
I’m not trying to be condescending here, but I’m just asking what someone thinks is happening here and what they can do with information scanned on your network.