dismount is a big no from me. You don't have to dismount and in practice it's not required. We aren't mapping right of way here. It's going to impede routing a lot.

My suggestion is simple
1) If the we are connecting footways without bicycle access tags, we shouldn't care about bicycle access on a crossing, no need to add it.
2) If we are connecting ways with bicycle access and it's a usual zebra, we add bicycle=yes
3) If we are connecting ways with bicycle access and it's marked with one of the three ways bicycle-pedestrian crossing is marked, then it's bicycle=designated

The advantage of this is that you can see everything from aerial imagery.

This is of course if crossing is mapped separately at all.

About unmarked crossings, they aren't that often mapped as separate ways, but if they are, I think they usually should inherit access tags from connecting ways. Unless it's a crossing with high kerbs, probably not a bicycle=designated.

In the example I've linked https://www.openstreetmap.org/way/1115986757 I wouldn't add any bicycle=* tags