Hello Muralito, thank you for informing me about the specific tagging utilized for these private streets. I will update the access tag accordingly for https://www.openstreetmap.org/way/1365335868. I classified these roadways as service as they seem to fit the OSM definition for service “ways used for vehicle access to a building, parking lot, service station, [or] business estate” (https://wiki.openstreetmap.org/wiki/Tag:highway%3Dservice). However, I agree with you that some of these additions, such as driveways, are not valuable in many cases, and I will be more aware of this moving forward.
If you have any other knowledge to share regarding service roads in this area, I would value any community feedback!