Sound like your new stalk could be shorted internally.
Early BDR wiring diagram here:
Disconnect the plug, set your meter to ohms. Connect one lead to the power in pin Grey
Connect the other lead to the Left pin Green. Meter should read OL (open)
Flip the lever to the left. Meter should go to Zero.
Flip the lever to the right. Meter should go OL. If not the fault is in the turn signal assy.
Alternatively the Yellow (right) and Green (left) pins should not have continuity to each other.
You don't perchance have a toggle switch labeled (or unlabeled) hazard? If you do, when its ON it shorts the L-R sides together to give you 4way-flashers. That's how I wired mine.
Only other item I can suggest right now is verify your plug is pinned correctly.
https://www.jbugs.com/VW-Tech-Articl...67-Wiring.html
Last question, Is the issue with the Blue and amber dash lights flashing with turn signals still there? or resolved?