Last Update:
After the hardware repair of the audio chip my IPhone works perfectly again.
Finally I paid 80€ and it took about 5 days to have it back. Much cheaper than a new phone. However, there are guys offering the same repair for less than 50€ but some of them seem to do the “quick fix” - just heating up the chip and not actually rebound. This might work or not .... some actually “fry it to death”. In Germany the range of cost for the exact same repair is between 45€ and more than 200€ - crazy. So keep your eyes open. Last comment: If you observe the described symptoms no software update will fix it - you will need the repair!!
Good luck :)