Hmm, it worries me a bit that you have no local social contacts, because that helps things so much. Where are you based? Most larger towns will have a branch of the International Women’s Club, and the members there will be able to give you far more helpful relevant info for your specific area. Or take a look at Toytown Germany online - the large cities also have specific sections there.
The caveat for all my advice is that I had my kids here yonks ago, so things might have progressed in the meantime. And I had mine at a birth house rather than a hospital, precisely because I found the hospital settings unnecessarily clinical but still wanted a medical setting with two midwives.
I went to both pregnancy yoga and a Geburtsvorbereitungskurs - maybe find out if either of those are offered in English near where you are. After the birth you are entitled normally to do a Rückbildungskurs starting 4 weeks after birth (basically a weekly mother/baby yoga course specifically to get your organs back in the right place). It’s possible that the insurance will pay for all three of these, so you’d need to check if yours does cover them - even if not I would do it in your position if you can find it in English, because I think the social contact would help you..When my babies were 2 months apiece I also went to a mother/baby class called PeKip, which is nominally to encourage baby development but is actually all about bored middle-class mums socialising. DH took DD1 baby swimming too, that was ‘their’ thing.
I’m a bit surprised you don’t have an appointment until after 11 weeks. Is that with a gynaecologist or at a hospital? For both my pregnancies I went to the gyn as soon as I knew I was pregnant and she did a scan to check that all was as expected, and that it was a singleton. Then you get another at 12 weeks, and I had one at 16 weeks and then the high def one at 20 weeks. The 20 week scan should be done at an obgyn practice with a doctor who is specialised in pre-diagnostic medicine, to look for anomalies.
So what kind of insurance do you have then? If it’s American presumably it’s some kind of private care, and they are often more generous than the ‘gesetzlich’ insurances ( my friend who was privately insured automatically got a private room instead of one with two beds, for example).
One thing I will say is that German healthcare is technically way better than in the UK, but there is far more responsibility on the individual to arrange where to go and what to do. So you need to be looking yourself at all the local hospitals and look for reviews, go to open evenings, ask searching questions about their c-section or epidural or water birth rate, depending on what you prefer. That’s why recommendations from an international women’s club would be helpful.
You need to be looking for a good Kinderarzt already, there are multiple tests (Untersuchungen) throughout childhood, and the U1 is straight after birth in hospital, the U2 is at 6 days if I recall, so you need to arrange who will do that if you’re out of hospital already. Our Kinderarzt came to do a home visit (which is otherwise very unusual for German doctors).
best of luck with it all, and do stay in touch on the thread if you need any more help.