Welcome. There are different "English" languages spoken throughout the planet. I wish to determine if the English language words we (North America) use are the same that you (Europe) used to describe the unexpected movement.
By "...transverse (perpendicular) play..." are you describing the flange being able to move, without rotation, towards the front and rear, and/or to move up and down? There is no push in and pull out (to the left of the car or right) play on the axle flange's rotation axis?
By "... radial play is absent." are you saying that there is no unexpected rotational movement (What I'd recognize by the term of "back lash") of the output flange?
This JCR transmission is one of a large family of VWAG transmissions and is probably not unique to the TDI engine. Other VW or Audi web sites that are more inclusive (not TDI focused) might have a larger pool of members and a greater chance of being a better source for your transmission condition evaluations.