This problem is persisting with complex ones i've noted other one time too...so for this there's 3 layers of dependency on parenting
1 - base which is deform (which is totally child constraint of target bones layer) - and no other constraints to keep it clean
2 - target bones which are affected by MCH
3 - MCH bones (involves IK) - which are affected by controllers

so when i bake the base deform only, it doesn't bake correctly only where the rig is affected by 3 layers i.e. on the tube attached to gun and back of the character.

but, if there are 2 layers on other parts of the body ( Deform < Target) baking works well

I was getting different results on deform of that tube bones when i parented it to "Palm" vs " spine" (none of which were correct)

If I'm not wrong, the baking should happen globally - as is on the bones?

Also, i think the error might be for stating missing plugins as everything in the file has been cleaned up (no orphan data as such)

Apologies for this might seem confusing...I'll post with video and images with detailed explanation in some time

Ah true true.. sorry will keep that in mind too.. i think the file is re-uploaded by Richard which is simplified .. will remove my previous comment which was kind of confusing

So after some digging, I think the problem lies in the way it's baked :

It correctly removes the constraints on the Deform bones ("Copy Transforms"), but then parenting is followed i.e. it's affecting the scale of parent (in the hierarchy) on the child (even with offset)

After the baking, the bone scale and position should be absolute - It should counter the scale as per the visual transform

What worked but not the best solution: Remove parents from all deform bones and bake.

If there's some complex rig structure, flattening the hierarchy may not be the best thing with many bones.

Even the simplified example file is far from minimal. The existing animation is hidden in the dope sheet (by having "ctrl" in the channel search box), there are invalid animation channels, and there are bone groups that may or may not be relevant, and certain relevant bone layers are hidden. I think also half the bones can be deleted while still showing the problem. To illustrate, this is what the dependency graph of this file currently looks like:

It really helps when things are properly simplified ;-)

Having said that, Visual Keying is known to be problematic, especially in the context of inverse kinematics constraints. Also see T76791.