> when some random small website
It could be some random website. It could also be a 3 letters agency website training airport security face detection, a social engineering website, a random website storing images in a public s3 bucket.
> The internet has reality distorted everyone's perspective.
You give all your personal / biometric info when you get a new passport. If some rando guy were asking for your biometric data in a street would you give him ?
3 letter agencies will kindly ask/force Facebook to share their face-detection data and algorithms, no need to do this themselves.
In fact I think the biggest co-conspirator of NSA and other agencies is Apple. First they put fingerprint sensor inside Home button, so you can't avoid using it, and have to share your fingerprints whether you like it or not. Now that they captured enough fingerprints they move to FaceID, which sensors are so conveniently placed that you cant avoid having your face scanned, even if you don't ever set up FaceID for your own use.