Hello Moritz,
I am not Stefan, this is a friend.
The paths you mentioned are not official (OK, a part to the west of the lake may be official, but not the entire length as shown in OpenStreetMap). Cycling off the paths is prohibited, hence probably the footpath with clearance for bicycles. vehicle=no because cars also have a no implied. Actually, one would have to check the entire area from the ordinance, but this is quite large. In the LSG, the following applies: cycling off the official paths and in the NSG: cycling off the public roads or paths. Cars are generally prohibited without signposted access. Best Robert