Does the Apple Watch really identify "you"?

As far as I can tell its just means as long as it's connected via bluetooth and in range. There isn't a Touch ID scanner on the watch or anything like that so I don't think that it forms an knid of "signature" to you.

It’s unlikely even the Apple Watch series 6 is trying to differentiate one human wrist from another.

• resting heart rate, ECG traces, walking gait analysis from the accelerometer, blood oxygen levels and pulse profiles, recovery heart rate and calculated VO2 max calculations all might be very personal and tell which wrist a watch is on, but I see no reason or need that Apple is collecting or trying to identify us with watch sensors.

I interpret the watch being connected to you as it can tell that the clasp is secured to a living human wrist and then can detect when the strap comes off that living human. Apple calls this feature Wrist Detect

So, if you were to put the watch on your friend and then authenticate Apple Pay - they could use your pay token for as long as the battery lasted and the device doesn't detect removal from their wrist. Similarly, that friend would now unlock your Mac as if you were wearing the watch.

I suppose Apple could try to determine if you have an extensively dark sleeve tattoo, but I haven't heard reports of that changing pairing and only that it can affect accurate pulse measurements with some tattoos.

The documentation only uses you to mean a person. The documentation is written with an owner in mind, so it refers to you, the reader, but not so specific as to your singular identity. It is not possible to uniquely identify people through the wrist.

Any specific identification magic largely comes from communication with the paired iPhone.