This is a bit of an ironic example. There’s still a lingering disagreement about where exactly to place the highway=traffic_signal node: at the intersection node or at the marked stop line. Either approach is an abstraction: we don’t intend to place the node at the literal position of the signal along the roadway. Depending on the region, that could be at the near side, the far side, the middle of the intersection, or all three at once. (I sometimes use man_made=traffic_signals when I have some reason to micromap the intersection.)
At least originally, the choice to place stop and traffic signal nodes at stop lines had as much to do with avoiding relations as anything to do with semantics. The primary intent was to move the node away from the intersection, to disambiguate which street it belongs to. Over time, the stop line became the most likely “real” thing to place it over.
Anyways, to reiterate, when someone is standing at the curb, waiting to cross, we normally say they’re still “on the sidewalk”, not “in the intersection”, whether or not that part of the sidewalk is surrounded by a grassy verge. When a cyclist is waiting in a turn lane behind a stop line, even an advanced stop line, we don’t say they’re “in the intersection” yet.
Tagging the whole thing as a footway=crossing reminds me of the now-discouraged style of extending a bridge all the way to the nearest intersection. I still do it sometimes when I’m in a hurry, just as I sometimes extend the crossing all the way to the intersection of two sidewalks when I’m in a hurry.
