I've found the cause(s) of all this trouble.
Rough idle.
There were several causes. Firstly, the tensioner itself was faulty, and the tensioning element was worn out. The tensioner had a bearing failure. Also, the belt was no longer in good condition, and the pulley was constantly wobbling up and down when idle.
It generated such strong vibrations that they could be felt even inside the vehicle.
During the timing belt replacement, I noticed that the upper guide roller had a bearing failure and was occasionally sticking. It also made a whirring noise and emitted a squeaking sound when the engine was turned off (I always thought that noise came from the exhaust). The timing belt had only been on for 50,000 km. I think that the previous owner didn't replace the upper roller during the last replacement.
All the rubber components on the exhaust were worn out, and there was a small crack on top of the middle muffler, which also caused additional noise.
All those noises and vibrations sounded like the engine was knocking loudly. Several people have commented on it before, saying things like, 'It's making a lot of noise.'
But now it's certain that the problem had nothing to do with the engine or its settings!
2. Jerky/stuttering behavior at partial load in 5th gear (1500-1900 RPM).
I initially thought it was just a typical 'normal' engine misfire. That wasn't the case. When I removed the air filter housing, I noticed a valve with a hose connected to the air filter housing itself and another hose going to the vacuum actuator on the turbocharger. There was also an unused connection there. Then I searched around a bit and found a loose hose that was pinched behind it.
Hose connected... shaking gone. The 1Z now runs absolutely smoothly and no longer makes a rumbling noise under full load.
It's running like a normal car again now!
The time it took for the whole thing was about three hours

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I probably should have done all of that earlier

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A question of mine has not yet been answered.
Where is the main valve located in the ABS module?
Regards...