Regular animation doesn't work on the limb with 2 bone IK Constraint

I don't think this was reported? Or is it working OK for all others?
I get to understand that if we set the weight of the constraint (Or the rig) to zero, (I don't mean in the code. Just in the inspector), then the underlying animation should be working OK.
In the image below, even after setting the weight to zero, the left hand is stuck in the same pose throughout the idle animation (As seen in the image) or any other animation. The difference is, if set to 1, then it moves with the target, with 0 it doesn't move. (But still is stuck in the position).
I tried with 2023 beta as well as alpha (Alpha has the new animation rigging 1.2.0)

I think I found the issue, and a Workaround also for that. It is an irritating bug nonetheless.

There was(is) an issue "The TransformStreamHandle cannot be resolved" if I do the Animation rigging "Rig Setup" on the root. I believe this is a known issue. Seen a lot of posts on that. So I had to do the "Rig Setup" on the "hips". And it works fine.

But the "Rig Setup" created another Animator component on the hips. I already have one in the root. So I ended up with two.

My WAR is, when I want to disable the Animation rigging override and go back to the original animation, I also have to disable this second Animator. (Disabling the Rig Builder also worked).

I am going to mark this as resolved.. (Even if I am not convinced it is a "Resolution"). If I am not clear or something Please ask, and I'll be happy to share more information.

But anyhow, I just went back to the OnAnimatorIK for my purpose for time being.. as I don't want to touch the character / rig hierarchy.