The most private security system is one that records to a local Network Video Recorder (NVR) or microSD card, with no cloud upload. Brands like Reolink, UniFi Protect, and some Lorex systems allow 100% local storage. You lose the convenience of mobile alerts from anywhere, but you gain absolute control. No cloud breach. No law enforcement backdoor. No employee watching your cat.
In most jurisdictions, you are legally allowed to record video of public spaces (the street, sidewalk). However: Arab Couple fucking in hotel room hidden cam Scandal