Those are the mechatronic's symptoms. The mechatronic (the valve body plus control unit) can fail, and it shows as jerky shifts, refusing to engage, limp mode, or a gearbox warning.
Before spending anything, scan it. VCDS codes point to the mechatronic when it is the cause.
Two things to separate it from:
- Clutch-pack wear. The dual clutches wear like any clutch, worse if the car is launched or chipped hard. Judder or slip means clutch-pack wear rather than the mechatronic.
- Overdue fluid. The wet-clutch 6-speed DQ250, common on GTIs, wants a fluid and filter change every 40k miles or 60k km. Skipping it is the fastest route to trouble. The later 7-speed DQ381/DQ500 (Mk7.5 and Mk8) is serviced too; "sealed for life" it is not.
A failed mechatronic is a big-ticket repair, which is why on-time fluid changes are cheap insurance.
Tell me the gearbox (6-speed or 7-speed), the mileage and when the fluid was last done, and what the scan shows, and I can narrow it.