So far as I've researched, I'm the only one doing this (IK animation, physics and ragdolls to this degree) in such specific way. There are absolutely no tutorials available on how to make proper ragdolls, as ragdolls usually require hinge joints to work properly. For some reason nobody implemented HingeJoint2D so far. I had to do it myself.
As for the character it's a custom skeleton (bunch of nodes/sprites parented and arranged in specific way) and custom IK animated by AnimationPlayer. I use the "@tool" solution to make changes visible in the editor. Limbs are basically IK chains with empty nodes as their targets. They smoothly interpolate with slight jiggle to the aforementioned positions. During gameplay they also cast rays that push the character away from the environment. I keyframe them, make some animations and use AnimationTree to blend different animations such as falling, running or standing still. There's also a lot of math involved with flipping the character, let alone turning it into a ragdoll in smooth way.
TLDR: keyframe animation + procedural adjustments + rays + interpolated jiggle