I didn't like Germany at all , some individual, lovely, kind people,yes but the place, the society as a whole, not at all.
I wouldn't say that Germany is child friendly in terms of adults being nice to dc , which for me is what child friendliness is about. It isn't Spain or Italy and you don't get people stroking little dc on the head or joking with them and seeming to enjoy their presence about the place. I would say they are accepted and not especially liked or welcome or made to feel liked or welcome (other than by their own families). What struck me the most about Germany is how rarely you see dc smile. If people don't smile at them, I suppose they don't learn to smile much. I have never seen so many stony faced little dc, I really found it disconcerting. Even amongst themselves there never seems a whole lot of giggling going on while they play but lots of talk along the lines "you can't do this and you can't do that". For child friendliness you will find that Germans go to Denmark, Italy or the US, they don't really look for it at home.
In terms of bf in public, it seems ok everywhere, I have certainly never seen or heard of anyone being told off for it. Dc can and will be told off by all and sundry (as indeed you the adult will be too) but there is a certain level of loudness and robust play which is taken for granted. You see and hear dc in restaurants and cafes and that is generally accepted. Neighbours might not be so tolerant in their own homes, especially older people who have no dc at home -and if you live in a flat you have to abide by noise regulation laws (everyone does but in a flat you are more likely to annoy someone): things such as not using the hoover, washing machine at certain times of the day (12-2pm I think) and so on. Most of it is common sense but the "Mittagsruhe" thing was new to me.
IME there are a lot of old and not so old miseries about the place whose main goal in life seems to be to spread unpleasantness wherever they go. A great deal of these people seem attracted to jobs in the so-called service industry where they will amaze you with a total lack of service, all of it grudging in the extreme.
Really this is my overwhelming memory of Germany. It may nto be PC to say so. Nevertheless it is true for my experience. It's not a happy go lucky, fun-loving place. On the whole it is a bit staid and a controlling type of society which occasionally goes almost inexplicably mad - carnival etc. You have had a lot of positive posts on the thread which tbh I cannot really relate to but I don't want to entirely put you off. I would just say it is one way of experiencing the place but possibly not the most common one -a nd I lived in a different place to where you are going.
The majority of expats I met from every country intensely disliked living there but there were a few exceptions and those few were 100% categorically pro-Germany , perhaps to balance the general negativity. For the most part they were French. For a couple of years, it could be ok for you. It might be that it is absolutely right for you even long-term but I would at least consider the possibility that you will not like it.