rigilk3nt
Thank you. Keep in mind there is a delay before Graphhopper (and OSRM) see the changes.
I have no info about signs in this location. From the general driving experience on La Palma I know that it is rarely a good idea to prefer steep shortcuts over serpentines (this is especially true for tourists in rental cars.)
On the European mainland these gradient following Caminos would all be signed access=destination.
On La Pama it is more an implicit "You can drive there if you can handle your car, and your car handles the slope and you generally know what you are doing."
If highway residential is not enough, with a bit of fantasy these small Calles maybe fulfill highway=living_street. This is an even more router-deterring option.
I am also not sure what the speed limits are. Often, residential buildings are attached to the Calles/Caminos without sidewalk.