I hope I understood correctly.
It’s not the capsule that should follow the animation, it’s the other way round.
For example if you put a Backward animation to your Forward Input, it will show the backward animation even though the character is moving forward.
Basically you need to make the Capsule rise above the Ledge first, so that the animation can follow it.
In which case, did you actually make an Event for the actual Climbing after the Hanging Event?
Just adding an animation without linking it to a new Event will cause the animation to deploy on the same spot of the last event (which is what you seem to describe).
Basically you should have an Event for the Hanging (which you have), and a new Event to link the new animation to the actual Climbing Up (The Capsule above the edge).
Also if you already set up a ‘W’ Event for going Forward (as it’s likely), you should branch it and add the ‘Climb Up’ Event instead of making a new one.