public means “domesticated” streets which allows police to enforce traffic infractions. If a police officer can write a stop sign or speeding ticket in that neighborhood then the streets are public.
IOW gated communities are NOT no entry zones. The only true gated community with no real entry is fischer island with a resident only ferryboat.
Not sure what domesticated means, but it is my understanding and experience in VA back in the day as a cop that police can enforce state laws on any highway (meaning neighborhood roads too) which are paid for/maintained by the gov - local/state/fed. The only exceptions were, if I recall (and I am getting long in the tooth) reckless driving and DWI/DUI.
We had many private communities that had to put a letter on file with the local court authorizing PD to enforce traffic code on their private roadways.
Not trying to pound my fist and say this is gospel....just what I was raised on...someone else might have a different answer from another state.