Where I live, many towns have signed bike routes which indicate the safest way to get from one place to another via smaller streets, despite not having proper bicycle infrastructure. These bike routes are sometimes even a few streets and are not a defined, cohesive route.
Example:
I like to mark bike lanes on the map so CyclOSM and other tools can use it. But what is the best way to tag these bicycle routes? Can it be done similarly to bike lanes?
You would usually collect all the streets/paths involved in a relation with network=lcn (local cycling network) or maybe network=rcn (regional cycling network) depending on length. See Cycle routes - OpenStreetMap Wiki for more details.
It sounds like these aren’t well-defined routes with start and end points. In that case, tag the individual roadways with lcn=yes.
If it does have a start and end point, then you’d map a route relation, tagging it as type=Routeroute=bicyclenetwork=lcn and perhaps cycle_network=* if it’s part of a coherent system of similarly designated routes. But don’t create a single route relation for the whole web of streets just because of these signs.
In this case, this is the national standard sign for the very concept of an lcn=yes or bicycle=designated, so a network relation is probably overkill unless the whole network goes by a specific name that its users should know about.
The entire M series of traffic signs function as route markers, but information=route_marker is for tourism=information, which would be more appropriate for an off-road marker of some sort.