On the DCS NSW Topographic map the dashed line only goes on the short section from Heathcote until it meets https://www.openstreetmap.org/way/1377326848 where it then stops.

The DCS NSW Base Map doesn't show any track/trail here, only much closer to the railway line it shows a railway maintenance track.

The park Plan of Management document at https://www.environment.nsw.gov.au/sites/default/files/royal-heathcote-national-parks-garawarra-plan-of-management-220657.pdf does include a black dashed line for management trail near here, but it follows the railway line and I believe this represents the railway maintenance track we have mapped at https://www.openstreetmap.org/way/96051429 and not this "Roman Trail" way which aligns with the Strava heatmap.

I checked back against the 1955, 1972, 1975, 1980, 1983, 1984, 2004, 2005 historical imagery and none show a visible management trail along this alignment at any point, so it's not like this used to be a management trail which over time has converted into a path.

Based on all this I find it highly unlikely this is a sanctioned walking track at all, and certainly unlikely to be a sanctioned mountain biking track.

That said, I do advocate mapping based on what's on the ground and I don't have any on the ground knowledge here, but it seems more likely to be an informal/unsanctioned mountain biking track.

Using highway=cycleway for a technical mountain biking track is controversial, and usually reserved for non-technical cycling paths. Personally I prefer highway=path + path=mtb.