Strictly speaking, the west part looks like being used by 2 track vehicles in recent time with some gravel additive on top, making it at least highway=track, grade 2. For path I don't tag bicycle=yes as that is implicit.... all routers assume path is foot/bicycle permitted. I only tag when there's an exception else we can start mapping  millions of ways with bicycle=yes. Many signs here bicycle speed 'velocità moderata' or max 10kmh... try that on a simple bike without speed display :o)))). Latter wholly ignored by 99.999% including the cops.

Valhalla is quick, OSRM is slow GraphHopper the slowest. Got a path that at least a month later is still not routed correctly by GH. One needs a machete for that path. The start is even impassable... a 2m 80 degree slope with dense scrub. Whoever put that path there must have been on a downhill. There's lots of MTB oneway tracks for downhill only. The furgone brings you to the top, trailer with 10-12 MTBs in tow.

ciao