Bending the axle does nothing regarding the runout of the freewheel, as you expected.
Does the drive side flange wave side-to-side when the hub rotates? Unlikely but if so, the hub shell is deformed. If the wheel has been trued up since the hub deformation occurred, the rim can still run perfectly true.
Potentially the freewheel thread on the hub could be axially misaligned with an undeformed hub shell. Unlikely but if so, that should be pretty obvious (after removing the freewheel) by spinning the wheel and observing runout of the hub threads.
The freewheel might be poorly manufactured with its freewheel thread axially misaligned with the freewheel body (difficult to check). Otherwise (and most likely) the manufacturing tolerances of the freewheel bearings are too great. Given the cost, I would just replace the freewheel (and chain if noticeably worn) with a more consistently made freewheel.