For context, the word “sidewalk” comes from American English. To speakers of this dialect, the general notion of a sidewalk is one of the most basic transportation concepts, right up there with “intersection”. We learn the meaning of a sidewalk as kindergartners, more or less by intuition, based on the predominant construction practices here, which are obviously influenced by regulations. A sidewalk is a physical structure; the idea of identifying one by a road marking, sign, or legal code is completely foreign to us.
Yesterday, I encountered this sign at the approach to a bridge. The structure behind it was built as a sidewalk and remains one, even though today it’s closed to pedestrian traffic:
If OSM has repurposed the word “sidewalk” to refer to a related but distinct British English or non-English concept, particularly one that depends on a third country’s laws, then miscommunication is inevitable. It’d be as if Indianans commandeered the word “motorway” to refer to an elliptical auto racing track (true story). Maybe that’s justifiable, but if we want to settle these debates, we need to take a step back and explain where we’re coming from. What is the word, in its original language, that each of us is promoting? How is it defined, and why is this definition the optimal definition of sidewalk in OSM?
I don’t recall the video – version 2.0 was over five years ago. But a lakeside promenade, as you’re describing it, would only be a sidewalk if it runs beside a road that also rings the lake. It was probably just an oversight.
See the talk page discussion. You had unilaterally rewritten this gallery to suit your perspective, which apparently was not shared by whoever originally created the gallery. Both versions have caused a lot of befuddlement among North American mappers. To a less experienced mapper, it isn’t merely incorrect; it’s incoherent. But maybe that’s just because the gallery needs better examples and more explanation?
I think you’ve proved my point from the wiki talk page discussion. 
In the U.S., there have always been shoulders that pedestrians use informally. Even the states that categorically ban pedestrians from roadways still allow pedestrians to hug the edge of the roadway if there aren’t any other suitable pedestrian facilities. (Some states explicitly allow cyclists to use motorway shoulders for the same reason.)
As a fairly recent safety measure, transportation departments have begun endorsing the conversion of some shoulders to “pedestrian lanes” as a “quick build” precursor to an actual physical sidewalk. The only physical difference is the painted pictogram, flexible bollards, and some signs. The only legal difference is that pedestrians are no longer in a legal gray area for walking on one. If you haven’t encountered one of these pedestrian lanes before, you’re more likely to refer to their European counterparts as shoulders, even though they only visually resemble shoulders.
I’m not sure if this was irony, but for what it’s worth, various passages on that page indicate that shoulders aren’t exclusive to motorways. If they are, we’ll need your help coming up with another word for the majority of shoulders that aren’t along motorways and also aren’t primarily intended for pedestrians.
By the way, “traveled way” is obscure jargon. Most American English speakers have no word for this concept, but some might refer collectively to “the travel lanes”. To generalize:
- through lanes + turn lanes = travel lanes
- travel lanes + buffer + bike lane + street parking + hard shoulder = roadway
- roadway + curb + soft shoulder + verge/berm/tree lawn + sidewalk + greenspace + noise barrier = right of way
footway:right=lane seems like a pretty elegant solution to me. We don’t worry about renderers or routers mistaking a street for a cycleway just because it has a cycleway:right=lane tag; why should it be different with footway?