Usually procedural means that it just randomly combines pre-made level pieces. So it has rooms and hallways and stuff and it just attaches them together.
For the animation, most of the time for that type of thing it moves the character to the correct position and just plays an animation. But there’s actually tools so that you can retarget parts of the animation, like Ikinema, where it could take a regular animation of opening the door and then be able to make it so that the hand always positions itself to the door, regardless of where the character is positioned.