https://www.openstreetmap.org/way/39230702
has a traffic_sign=DE:250 when entering from the south-easterly side (Wallhausen).

My entry with:
foot=yes
bicycle=no
horse=no
vehicle=no
is therefore correct.

As I understand it, the entry of an "access state", so access=yes or access=no is not necessary at all for any path or track, and:
if NOT entered as access=no, than generally considered as access=yes, ... but excluding an "no´s" for e.g. persons, animals (horses) or vehicles (bikes/motorcycles/etc.) entered as =no.