A few things can cause it, duff injector/s, turbo, egr....first thing is get codes and take it from there. Mine was similar (also mk3 2.0tdci) but had been sitting for a month or 2 and had a split in the egr/intercooler pipe so wasn't getting full boost then when a new one was fitted the soot was bad but only for a few miles then cleared but yours is obviously different as the smoke's there more or less all the time.

But get codes first, just to say, it probably won't tell you specificaly injectors if they're duff it'll just say fuelling issue ie low ect but codes will help.

I've also just fitted and coded number 1 (left) injector and got a recon for number 3 ready to go in as it was showing signs of leaking too. It's smokey staring from cold too so hopefully this will fix it if I'll be renewing all 4 probably.