Do not buy another consumer-grade extender for that link, it’s the wrong tool for a fixed 120ft point-to-point hop. What you actually want is a proper wireless bridge pair, Ubiquiti’s airMAX line (NanoStation or PowerBeam) or MikroTik’s wAP series will both wildly outperform any off-the-shelf extender at that range, especially through wood with no metal in the way.

Point one unit out from the house, one at the cottage, run them in bridge/station mode instead of repeater mode, and you’ll get close to wired speeds since it’s a dedicated directional link instead of a shared radio also serving normal WiFi clients. Should comfortably handle the camera at full resolution.

Costs more than a $40 extender, but a used NanoStation pair runs cheaper than trenching, and attic mounting like you’re already planning is exactly the install these are made for.

Almost certainly leftover reference-firmware laziness, not an actual requirement. A lot of cheap WiFi-radio modules ship with a default setup-AP mode meant for initial onboarding via a companion app, and a lot of OEMs never gate it behind a real first-boot-only flag, so it just stays broadcasting forever.

Since you can’t disable it or change the MAC, containment beats fixing it: block that MAC at your AP/controller so it can’t associate with anything, or isolate it if your AP supports MAC-based assignment. Doesn’t stop it broadcasting, but stops it being useful to anything nearby.