It's modelled as part of the cycling network, and where they exist; bike infrastructure has been captured on the bits of road.

https://www.opencyclemap.org/?zoom=15&lat=-34.91788&lon=138.64144&layers=B0000

I agree it feels like it could be highlighted better as a more explicit "bikeway" as described here: https://www.npsp.sa.gov.au/our_services/major_projects/beulah_road_bicycle_boulevard

Not really any specific signs call it that on the ground though,