There is a sign but access talks to whether the road is physically restricted (gate). From the Wiki: “Note that access=private is intended to indicate that access is restricted, not whether the object is privately owned or not. Use ownership=private or operator:type=private to record this kind of status. For example, a privately owned road with public access may be tagged like any other road with public access – without access=* tag, or with the explicit access=permissive.
Unfortunately as of 2023 access=private is widely used as a duplicate of access=permissive as well as ownership=private and should not be expected to match the originally intended meaning.”  In my survey, each house receives mail delivery as well as trash and recycling pickup. This and the fact that the roads were wide open without any gates led me to feel that “access=permissive” (which is how they were previously tagged) is the most appropriate. 