Physics Grab

What I linked would definitely work for grabbing things, especially that you could have the handle attached to a bone / socket.

[…]i don’t think this could be of much use for
something like climbing, which is the
part that i find the most complicated
to implement.

Animation is not my field, not sure how it’s done. While I do know the game, I honestly don’t know how to replicate something like that. My best guess is a form of physics constraints.

If you wait long enough, someone more knowledge should chip in.

This seems whacky and promising: