How do I make interactable animations on Rigs

So I am making a vr game and I was wondering how does games like Blades & Sorcery make their AI’s Model be interactable while being animated, like if their standing still, you can move their arms by pushing and moving it, I’ve tried active ragdolls, but that didn’t give the effect I wanted.

Active ragdolls is probably the only way to go. Now this is a very wide field with many different approaches, you just need to find the right one for your use case. It can also get pretty complicated, as there is a constant fight between staying close to an animation and reacting to in game physics.
If you are not very experienced with physics you can try an asset store solution like puppet master for this purpose.