That is a nice video. Thanks for putting that together. There is a very detailed procedure in the Factory Service Manual for adjusting all of the control linkages. Some of it requires a special measurement tool, but most of it you can do without anything special. I just checked and it does not appear like the w115 FSM is readily available online right now. Someone publishes it on occasion, but I could not find a copy quickly.

In your case, the issue is obviously temperature dependent, so I don't think it is linkage related. Somehow, the car appears to be getting more fuel when warm. So I guess it could be a problem with the injector pump, the air filter oil being consumed, the crankcase oil being consumed, or some sort of fuel like blockage that relaxes as it warms. The vacuum line from the intake manifold to the vacuum pump sometimes can carry oil up to the engine from the vacuum pump (front of engine, not the injection pump). Your line looks dark up top (oily?), but not obviously bad. There is a diaphragm in the vacuum pump that can tear and release oil where it is not supposed to go. Look at that line and see if oil could be traveling up it to the intake manifold.

That vacuum line from the back of the injection pump to the butterfly valve can also leak and cause problems with idle. Or a diaphragm inside the injection pump can do the same. I forget the details of how to check those, but they are here on PP if you dig around.

Good luck. Hopefully some of the experts will weigh in. I own a similar car, but am not super knowledgeable.

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1968 220D, w115, /8, OM615, Automatic transmission.
My 1987 300TD wagon was sold and my 2003 W210 E320 wagon was totaled (sheds tear).