There's a lot of back and forth here about the torsion beam rear axle versus IRS, with many people saying the beam rear axle cars are inferior. I understand that view, but these are front drive, nose-heavy cars, which isn't the best place to start for excellent handling.
If you want to make the '16 TDI more fun to drive the first improvement is a rear anti-roll bar. Get the stiffest one you can find, preferably one that fits inside the rear axle beam. This will lighten the steering, improve turn-in, and reduce understeer. However, it will also make the car more inclined to spin when it's slippery out.
Second improvement would be to improve front camber. I don't know how much adjustment is available in the stock suspension (usually none) but if you can get one degree of negative camber it makes the car much more responsive without negatively affecting tire wear.
Third is better dampers and, more important, better tires, which you appear to already have. The lower the tread wear rating on the tires the more stick they're going to have.