Upon further investigation I find that the value in lookup is as expected and the below also switches the constraints on and off.
LD.AreSegmentsEqual = True
In my view given the paragraph below the correct situation should be that the visible dimension object should not report the status of equality only have a function for creating an equality constraint. Currently the property acts as a toggle so you can set it to True to first add a constraint and then to True again to remove it. That seems wrong but is probably related to the fact the Dimension class represents both Dimensions and Constraints. i.e. it is valid to read such a property on a constraint object but not on a dimension (should be Read/Write on constraint and WriteOnly on dimension).
Filtering for constraints and matching the items in reference array may be an approach to identify if the elements are constrained. Note however that dimensions are not dependant on constraints and constraints are not dependant on dimensions. So you can delete either without affecting the counterpart (there is no actual relationship and so would not expect .GetDependantElements to report one). Probably every Revit user has encountered the following when deleting dimensions set to equality:

You can also do the converse by deleting the constraint in the UI. After doing so the visible dimension will still report equality until one of the segments is dragged (it becomes an indicator of equality at that moment only not a constraint).
You can review the ValueString (EQ), Value (Same for each segment) and ValueOverride (Empty) of each of the DimensionSegments to know if the Dimension was once constrained to equality.