my wife is a German citizen and has been living in the USA with an H1B since 2015. The H1B was extended in 2018 and is valid until October 2021. Currently the Greencard-Process (EB3) is running, but we are still waiting for the Prevailing-Wage-Answer (so the process is still in a very early stage). So it will be a long time before she gets her green card.
My question: Does the greencard process have to be completed when her H1B expires or do you get some kind of “toleration status” when the I140 is approved?
No need to have it completed. As long as you have it started before 1 year of 6 years of total H1B, you will be eligible for either one year or 3 year increments depending on where you stand in green card process. Check USCIS Guidance and below screenshot from the same document.