I understand the problem now, when you said you activated the horn with VCDS I thought you then pushed a button and it worked. As the coding seems OK and the buttons are working, I suspect it is a wiring problem.
Here is a photo of my loom -
View attachment 73093
It is for a Polo (part number 6RD 971 584 D) and I had to change one of the horn spade terminals as it was the wrong size. Do you have all 5 wires going to the black connector - especially the blue/white wire? Hard to tell but looking at the photo the order is brown, black, purple/white, blue/white then grey. The blue/white wire when connected to the brown wire should sound the horn. Try this (by touching the spade terminals together) incase the horn switch is not making properly. Check continuity from the spade terminals to the black connector terminals. Also use VCDS to see if it shows the horn switch signal change. As Mocko1962 said above, some photos of the loom and the instructions would be usefull.
Here we go , i will try to explain the best i can
( metering across airbag horn contacts show contacts ok when pressed)
Pics won't really help as its all taped up and all wires white
Specific set of cables for the retrofit of an original multi-function steering wheel (MFSW) from VW
www.kufatec.com
This is the loom used, all wires white with labels. added to original loom.
(Original Blue/white wire removed both ends Spade one end pin 8 of clock spring the other end)
New loom:
clock spring join wire, pin 7 (brown ) - join wire that goes to pin 1 on black connector
clock spring add wire, pin 8 (removed blue/white) - pin 5 black connector
clock spring add wire pin 09 - goes to pin 3 black connector
clock spring add wire pin 10 - goes to pin 2 black connector
black connector pin 4 - (spade terminal) goes to where blue/white was removed
If I touch the spade terminal together nothing,
i do have all 5 wires in the black connector.
I can't find the measuring block for the horn switch only an out put test.
At then clock spring the instructions link pin 7 (brown wire), Via the left hand switch
and pin 8 horn (Blue/white), if i touch these nothing.
Anybody got a pic of the inside of their clock spring plug with coloured wires as above?