Hi, ElliottPlack!
My name is Polina, and I’m a mapper in the OSM team at Lyft.
The key difference between the access and motor_vehicle tags is that “access” affects pedestrians as well. Therefore, I agree with StreetSurveyor's edits that it would be clearer to use motor_vehicle=private here.
However, since pedestrian paths along the road are already mapped as separate ways in OSM, and there is a sign stating 'Authorized vehicles only' as seen in a Lyft-owned image (https://drive.google.com/file/d/1CJUYin38UvV5fS3kLtE9WXF1jcutgnvB/view?usp=drive_link), and at the time of our edits, the bicycle=yes tag was present, adding the access=private tag also seems acceptable in this context.

Best regards, Polina.
