From what I can tell, Parent Constraints in Local Space do not seem to work as I would have expected.

Expected Behavior: Position and Rotation Values should be copied from the source, weighted and then pasted into the target.

Current Behavior: Rotation Values are working correctly, but position values have a large offset in the Local Y Direction.

In the specific example I was looking at, the source had an offset of

X = -0.23

Y = 0.00

Z = 0.04

But the target (result) had a position offset of

X = -0.03

Y = 1.33

Z = 0.05

I used a weight of 1 with only 1 source and the parent objects for each of these were offset by the following amount from their parent:

Position:

X = -0.01

Y = -0.83

Z = -0.16

Rotation:

X = -1.73

Y = 91.71

Z = -82.79

When using a Position Constraint and a Rotation Constraint in Local Space, I DO seem to get the correct result. So I think it's just an issue with Parent Constraints specifically.

In the example I was testing, I have quite a bit of other things going on in the scene, but nothing that should have affected this function. I have only tested this in the editor for the moment, with version "3.6.2-constraints.1"

Please let me know if you need any additional clarification.