Hi offissa,

Welcome again, see also my other comment.

I travel this road almost every day by bike and I am quite sure there is no sign that forbids using that road by bike, horse or on foot.

One could discuss is one should tag "use_sidepath", see https://wiki.openstreetmap.org/wiki/Tag:bicycle%3Duse_sidepath
That is probably correct, if you enter the road from downtown Metzingen.  Coming from Maienwaldstraße, however, there is no sign legally forcing you to use the separate path.

What's your opinion?

Best regards
Metzor