It’s doubly confusing on access=private as
https://wiki.openstreetmap.org/wiki/Key:access
and
https://wiki.openstreetmap.org/wiki/Tag:access%3Dprivate
sort of contradict each other.
The first one implies more to do with what is supposed to happen
“Access values describe legal permissions/restrictions and should follow ground truth; e.g., signage or legal ruling and not introduce guesswork. It does not describe common or typical use, even if signage is generally ignored.”
whereas the 2nd one
"Note that access=private is intended to indicate that access is restricted , not whether the object is privately owned or not.
Practically (at least for me in the UK) if there is a “Private Road” road sign but there is no gate (or always open) then almost always you can “physically” access it on foot and indeed such roads often have cut throughs to designated public footpaths. So think what was suggested above as motor_vehicles=private and foot=yes largely describes the practical access and indeed the second article even says " 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. Problem is I have never seen the ownership tag being used