Great suggestions made. I'd like to add the following.
1.Injectors - possibly
2. Sensors - coolant temp, radiator lower hose temp, Maf - test with a multimeter and vcds
Valve stem seals - maybe
Turbo oil leak- maybe
Vacuum leak - maybe
Torsion value - maybe
Air in fuel - possible, by adding a clear hose just before the tandem pump using an 8mm straight connector (copper pipe) to join to the existing fuel line at one end of the clear hose and jam the other end where fuel line was disconnected. (You'll have to loosen both 10mm bolts to temporarily release the metal fuel lines).
Go for a drive park up overnight.
Get an assistant to start the car the next day while you video the clear section of pipe with your phone.
Hopefully no bubbles.
Best of luck.
This is a super low cost diagnosis technique.
A totally sealed fuel system is required on a tdi.