Bathtub flow valve - does not close

The rotating element on the edge of the tub acts on lift rods that raise and lower the lock. If it doesn’t do that, then the screw on the lock is misadjusted or the lift rods are not well connected to each other.
The lock has a snap-on cap for better appearance and a smoother surface. You can turn this, but it has no functional purpose.

So that means if I remove the lid, i.e. the white part with the screw, and then turn the rotary knob, I should see the white part (screw) move up or down?

That means if I take the lid off, that is, see the white part with the screw, and then turn the rotary knob, I should see the white part (screw) move up or down?

That does not happen.

I cannot clearly understand from your statement which screw / which "regulator" you mean. You have a rotary knob on the inside of the tub near the overflow. This raises and lowers the closure. On the closure itself, you have an adjustment screw that acts statically. If this adjustment screw is turned out too far, the closure cannot fully lower and water leaks out. If this adjustment screw is turned in too far, the closure cannot be opened by the rotary knob and should be watertight.

You have a rotary knob on the inside of the tub near the overflow. This raises and lowers the closure. On the closure itself, you have an adjusting screw that acts statically.

Do you mean with closure the part I have now marked in red in the picture? If so, nothing happens when I turn the regulator at the tub edge, nothing moves at all. Do I then have to readjust the screw and how do I do that best, since I can’t grip it with a normal screwdriver.

You take out the white part which you circled and check if a lifting mechanism moves underneath when you operate the rotary controller on the edge of the tub. If yes, then the white part with the metal pin must be adjusted - this should be possible with a screw held in place by a locknut. If not, you need to get to the mechanism of the lever system. Usually, there is a maintenance hatch for this; otherwise, the only option is to knock it out. The most cost-effective solution is to remove the current closure and use a simple plug like in the old days.