I have mapped overlapping area:highway=footway + area:highway=primary areas for crossings like this in the past. The area is actually both at once, so it’s not incorrect. Some of the examples in one of the the original area:highway proposals [1][2] actually have overlapping area:highway=* areas and the proposal mentioned this:
Areas for lanes (e.g. area:highway=bus and area:highway=shoulder) should be drawn inside the area of the highway they belong to. Parallel ways should each get their own area (e.g. dual carriageways, cycleways if drawn as separate ways).
Afaik this practice is currently not really in use however and shouldn’t be seen as the definitive way and is still open for debate. (The original proposal was never actually officially adopted and area:highway=* is so far mostly just used in the obvious cases with a single highway type.)
Combining both highway types in the value using the usual semicolon notation would be another option: area:highway=primary;footway. I would much prefer this over trying to find single tag values (e.g. area:highway=crossing, area:highway=junction, …) for every possible combination. The details like ‘crossing’ or ‘junction’ can be added with additional sub-tags. (area:highway=primary;footway + junction=yes + crossing=marked) This also solves the issue of an area being both a crossing and a junction simultaneously. It also keeps the values for area:highway=* corresponding to the underlying highway=*.
The proposal has this to say about junctions:
Junction areas: area:highway= with junction=yes/roundabout/y_junction