Golf Vibration During Warm-up (60-90° ASZ)

After finally saying goodbye to my old car (it was about time ), and getting a new Golf with a 96 kw diesel engine, I have a question:
After having thoroughly reviewed the entire forum and finding no clear solutions for...
I've found my problem (but not with VW), now the question is...?
Can something useful be made by oneself?
Are there any solutions from Volkswagen yet?
And one more thing: If my car is parked for longer than 3 hours, and I...
When he turns the ignition key, it makes a noise for a few seconds, as if...
a pump that grinds sand somewhere

There is a new software version for the engine control unit. However, based on all experience, this doesn't improve anything. In fact, mine started to exhibit jerking after the update .

The scraping sound is coming from a fuel pump that activates in the Golf when the fuel level is below approximately 50%. This is perfectly normal.