When sidewalks are mapped as separate features, they often cross service roads, e.g. parking lot entrances. When they do, there is often no gap in the sidewalk. The wiki page for highway=crossing doesn’t mention this situation and makes me feel like the tag wasn’t intended to be used this way. While it is technically a crossing, tagging it as such seems unnecessary, especially when it results in StreetComplete asking about islands, tactile paving, etc.
The tags crossing=marked/unmarked also don’t seem appropriate here. Maybe a new tag is warranted, such as crossing=sidewalk?
I would call it a highway=crossing + crossing=unmarked (unless it is marked) but I see the example and know what you mean. It isn’t really a crosswalk type crossing. I think mapping it as some kind of crossing would be helpful to a router to say that there is a obstacle here.
It looks like the tag crossing=pavement is being used for this sort of thing, see example here.
There is a bit of discussion here, https://github.com/openstreetmap/iD/issues/8463 - mostly about driveway type service roads. I guess, for routers that is as much helpful, as it would be to tag a node highway=intersection everywhere, where two roads cross (something we do not do.)
Certainly, a key to distinguish such non-descript non-crossings from places where pedestrians cross real streets will become much wanted, once the dilution of the meaning of crossing gets widespread.
I would only set highway=crossing if the service road interrupts the sidewalk. If the sidewalk continues uninterrupted across the service road, as is often the case with driveways (i.e. it is more like the cars cross the sidewalk, not the other way around), I would consider it incorrect to tag the shared node as highway=crossing.