Characters able to climb ledges

I’m trying to make a fairly comprehensive locomotion system using A*. Something similar to XCOM where characters can vault above covers (so path from pathfinding goes through covers and trigger a vaulting animation), as well as climb on ledges.

The climbing on ledges is the first goal I have. Right now I have basic pathfinding working through a Recast Graph (I want freeform movement, not tile based). I would like characters to be able to climb on ledges that are equal or less than their height (so standard character being 2 units high, they should be able to climb on any surface that’s between 0.1 and 2 units higher than them) and play an animation doing so.

How should I go about doing this? I toyed with “Climbable Height” but it messes with the graph, and I want these cases to be considered as “special” cases (a bit like node links, for ladders for example). I also don’t want to be placing everything manually to indicate that you can climb from this point to this point, though maybe my prerequisite are too high/ambitious?