VW Caddy 2K Engine: Black Smoke When Accelerating

I have a Volkswagen Caddy, manufactured in 2006, with a 1.9 TDI engine, 75 horsepower, and 110,564 kilometers on the odometer.
"For about 10,000 km, the Caddy has been smoking, but only when accelerating under load, for example, when starting or during gear changes. The smoke is extremely black."
Lately, it's started to idle roughly (and sometimes runs on only 3 cylinders).
Okay, now let's talk about the activities that were carried out.
AGR valve replaced, Mass Air Flow sensor replaced, Turbocharger pressure sensor cleaned and functioning correctly, Turbocharger inspected and functioning correctly.
Charging pressure system checked for leaks - OK. Error memory read - no errors found. Compression pressure measured - OK.
VW says that the PD injectors are not working synchronously, or that the injection amounts are too different, and that they need to be replaced. Is it possible to check the PD injectors for residual dripping or to test them in any way?
Best regards from the beautiful region of Bavaria.
Hanni.

What is the lambda value (air-fuel ratio) at low RPM under full load? I suspect there might be a small leak somewhere in the lambda sensor circuit. This is noticeable despite the low lambda value, due to the high air mass flow.
It could also be a stuck EGR valve that isn't closing completely, which is causing the air mass to be below the expected value.

I don't think the PD elements are defective; I believe the rough running is more likely caused by a faulty EGR valve.

Take a look at measurement block 13 while the engine is idling...

Okay, the AGR valve has already been replaced; the old one was completely carbonized, so we can rule that out. All the turbocharger boost lines have been checked for leaks and inspected, so they are also not the cause. The boost pressure has also been checked once with the vehicle's built-in sensor and once with an external pressure gauge.
When I removed the vacuum hose that activates the turbocharger (vacuum actuator), all the symptoms disappeared. The only side effect was that I lost power because the turbo was deactivated.
Best regards,
Hanni

Hello, you're a bit off track. Black smoke from that engine, in its standard configuration, only occurs if either the intercooler/charge air duct is leaking or the EGR system is faulty.

Please provide the values from the MWB 13 diagnostic trouble code (DTC) table so that we can rule out any defects in the engine or pressure control (PD) units.

"If there's any questionable tuning installed, I would expect that to be mentioned. We're not in kindergarten here, and specific values will eventually reveal the truth anyway. It's just frustrating when such fundamental things are kept secret."

Best regards, Rainer.

So, there's no performance tuning installed in the engine; everything is stock.
The AGR valve has already been replaced, and the intercooler piping is also in good condition.
Pd elements should also be excluded.
Currently, I don't have any values because the car is at the Volkswagen dealership.
My question is: If you disconnect the suction hose at the air filter (after the MAF sensor), will everything be okay again? (The MAF sensor has already been replaced three times.)

Problem solved: The EGR valve was not installed by the original manufacturer but by a supplier company.
Now, the AGR valve is sending incorrect values to the control unit (which were not stored in the error memory), and this is changing the injection values.
The new AGR original part from VW was installed, and everything is now working correctly.