Hello, I drafted the parking=streetside proposal. You can use it anywhere where the documented properties apply (a parking area off the side of a road lacking dedicated ways), not just on public roads.

Access is totally separate from the parking area classification, and here access=customers should suffice.

Don't worry about routing. This rarely presents a problem (most POI's on the map are not connected to a road and as mentioned above, routers tend to bridge small gaps just fine), and people don't usually route explicitly to parking bays in any case.