Firstly congrats. She's here, she's safe and you are in a country where formula is available if you need it. Try and stay positive.
Secondly, using formula doesn't mean you've failed or that you are shit parent or that you wont breastfeed.
Hand expressing is far better, if milk hasn't come in, rather than pumping. Pumping colostrum milk is difficult, it is thick and not worth the effort to pump it (gets clogged in pump, only several ml will come out. Hand expressing (you tube it, or get husband to do as you need 2 hands and a syringe to catch it).
Her tummy size is that of a marble. It's small. It only needs small quantities of milk often. So feed, little and often. Your body works on a supply & demand system, the more she sucks, the more you will supply. I would not let her go more than 3 hours (probably even 2) without offering your breast for a feed. 6 hours is too long to let her sleep without feeding from you.
Retained placenta can hinder milk "coming in" so LOTS of skin to skin with your daughter - lie on the bed, both naked, keep a light sheet over your bottom half, and her face close to your breasts. Try a bath together too, the warm water on you may also help - your hormones (oxytocin) will help too, so keep her close to you, and remember how amazing she is.
formula can cock up milk supply if when you use it, you don't express. So, if you choose to use formula, try and hand express. Like pp said, the amount that comes out isn't necessarily an indication that you're not producing. The key is for your baby to extract that milk - they're far more equipped to do this than you hand expressing or your pump.
Have you tried the 'flick' technique? You hold baby across your breast with face / head near nipple area, and with your spare hand, you hold your breast upwards away from baby and when she opens mouth wide, 'flick' your nipple in to her mouth, aiming to get your nipple as far in to her mouth as possible.
In Germany, are there any breast feeding support groups? You need some real life support too - the above is only from experience of being a peer supporter - I'm not medical qualified at all- but be assured that if you need to give formula, you can, it isn't the end of the bf relationship. With time and the right RL support, you can bf fully or mixed.
Also, keep an eye on your bleeding. I had a similar delivery and manual removal of placenta afterwards (fucking painful...worse than labour). They didn't get it all out. I had a further operation (ERPC) when baby was 11 weeks. This is common I believe because they have to be care trying to get it out in the first place (ie could tear cervix wall). BUT if you have some left, it can hugely affect milk supply. I was asked this several times during the checkups and it didn't actually affect mine (over supply) but once removed I had over over over supply
so keep an eye on it (bleeding at 6 weeks, see doctor for check up)
Chin up, you're doing great 