Hi
Not sure if you have surveyed this, but I know it well.
I am not convinced this fits the definition of a busway.
The first paragraph starts with "Busways are not meant to be used by motorists, pedestrians, or cyclists.". Whilst there are no entry signs there is no restriction on foot traffic and routers should not be sending pedestrians the long way round to get to the surgery.
Whilst unclassifed was a bit OTT it is just a bus station where highway=service with appropriate access would be more appropriate.
Cheers Phil