In regards to taxation of a sale I can only point to this first google result: https://www.rosepartner.de/besteuerung-verkauf-gmbh-kauf.htm...
In cases where you personally owned the company, only 60% of the sale price will taxed. After this Teileinkünfteverfahren the 60% are indeed subject to your incomee tax. Even better as sales are consindered außergewöhne Einkünfte their taxation will follow the Fünftelregelungen where the sale profit is spread across five years. https://de.wikipedia.org/wiki/F%C3%BCnftelregelung Realistically you'll end up paying taxes comparable to the 10~20% you can expect in the US.
Edit: Sorry, missed that part about the seller GmbH still existing afterwards. But the next paragraph I linked goes into that as well: https://www.rosepartner.de/besteuerung-verkauf-gmbh-kauf.htm... Again, Teileinkünfteverfahren only 60% being taxed.