Do you also favor mapping them as separate ways? I think that’s really the definition that matters most in an OSM context: a sidewalk is a footpath associated with the street that can be mapped as a separate way without violating the physical separation principle (even if that isn’t the locally preferred style).
I was unaware that kindergartners in Germany are taught random English words such as “sidewalk” and that your local laws are written in English. 
To reiterate, if this American English word has been co-opted by German mappers as a euphemism for a more specific German word, and that word’s meaning should be imposed upon the rest of the world, then the documentation should say so.
I’m definitely not insisting that the whole project follow American English, but I think it’s very important that native speakers of other languages be aware of what can be lost in translation. That “sidewalk” happens to be a common translation of Bürgersteig does not necessarily mean the two words have exactly the same meaning. Defining sidewalk as Bürgersteige either requires mappers and data consumers to pay special attention to documentation, or it requires us to accept a little inconsistency from one country to another.
For the record, the sidewalk feature page was started by an American; the sidewalk documentation was started by a Swedish mapper; and the successful proposal for footway=sidewalk ways was written by an Italian mapper based on an earlier proposal written by an American mapper. But generally speaking, you’re correct that we’ve historically benefited from the German community’s insightful proposals and documentation about navigation-related tags. The earliest proposal related to sidewalks was indeed written by a German speaker: it controversially proposed calling them “footways”.
Anyways, to me, the dialectal vocabulary and wiki history are secondary. The most important consideration is whether the tag’s definition is practically useful. If defining footway=sidewalk in terms of function causes this pedestrian lane to require a bunch of tags to undo the essence of what footway=sidewalk was approved for – physical separation – then this is classic troll-tagging. For the pedestrian lane, I favor footway=lane on the roadway (not a separate way), because it follows existing patterns and is unlikely to trip up any data consumer that has been interpreting OSM tags correctly.