Do you know why the Russian engines gave black smoke? Because they found that fat and short combustion chambers worked best for their compressor design. After Safran helped them they managed to correct some of that shortcoming.
Our engines are designed with western tech. They probably will not give black smoke. Both TS1400 and TF6000 first ignition photos don’t show any black smoke.
Should TF35000 give black smoke, neither you nor I will know about it anyway. Also it is not the end of the world. It may be a mixture or injector fault. Today’s FADEC assisted engines control compressor and fuel injectors to give best and optimum mixture.
Boils down to insufficient capital investment (incl the RnD) needed in tail end of USSR days (about 80s onwards and then with russia inherited what it did in 90s onwards from this inertia/malaise). So short cut fix arounds with consultancy are there like you mention, but essentially the underlying capital machinery and process control is well behind Western ecosystem (which has its massive commercial expanse its deployed in for continued RnD feedback loop, past the smaller military one) now. Black smoke is just one thing you see, there is the availability rates (i.e MRO downtimes, MTBO etc) for the engines too, failure rates and so on.
If Turkey mostly relies on/leverages on western capital machinery + tooling and process control it has accumulated, it should be up to date. Rest depends on optimisation, lot of testing and refining a design.