OM602 2.5 turbo ticking sound at idle and low engine speeds

[seeyoulateralligator]

Hello everyone!
I've been reading this forum for a long time and I'm very inspired by the whole community that likes to understand and restore their old friends!

I have a 124th with an OM602 2.5 turbodiesel from 1992, which is an everyday car.
But there is some problem with the engine: after starting the engine, I hear its ticking on cold, which increases to 1400 revolutions, and then disappears sharply and the engine runs quietly. Only when warming up to 83-85 degrees, the sound noticeably subsides, but still remains a little.

Could this be due to the fact that before replacing the plungers, the car smoked under load and a carbon deposit could have formed, which creates poor combustion at low speeds? Sometimes after I stop for 5 minutes and then start the engine again and start driving, the power practically doubles, and then disappears.
Will the "Italian tuneup" help with this?