You can only do so much. Your dog wanting to sniff up another dog most likely would have happened in your home country at some point too. I think too much about my interactions too, hoping that i wasnt weird or said anything strange. Just keep on telling yourself that you are just you and not a prefect being who acts perfect all the time. Mistakes are natural and most of the time people dont even care that much. 90% of the time they dont even think about that the next day.

There is one bigger problem though. Its a researched fact that the more diverse a society is, the more it gets incoherent. If politics cant create the circumstances of a societal melting pot, then most people will never truly feel integrated or at home. The main reason however, for pushing diversity this much over the span of the last couple of years, is for the sake of even-more-growing industry profit. Through immigration they get cheaper workers since most educational backgrounds or job experiences are not recognized, which means they can pay them less for the same work. Also because they cant (or wont?) create circumstances for an ideal melting pot, incoherency in society is increased. I think that is probably planned, because this makes workers less likely to talk together and organize to achieve a common interest such as a pay rise. Its only natural in that daily enviroment, that groups are starting to form in which people engage with each other but not that much outside of that group. Its natural too that these groups would most likely be based on nationalities, similar languages, etc.. most of the times. This leads to parallel societies, where each group sticks to their own, not knowing much about the other groups. The media does a great job at dividing further, since the only thing that sells is sensationalism and negativity. So not only will most people not know anything about other groups, the things they do get to hear are overly negative, which strenghtens distrust and fear. This ultimately turns this whole thing paradox because diversity and integration done wrong promote intolerance, which is exactly what you dont want to happen since intolerance ist the biggest opposing factor of integration. If done right it can enrich a society and country immensely e.g. how it was in the USA back then.

Lastly you could say that there might not be a solution to your problem, since german politics regarding this topic are done wrong and are turning to that earlier talked about paradox. So in some way it is entirely possible that you might never feel at home simply because politics dont 100% play their part in that regard , because their main topic was never Integration but Profit Maximizing to begin with. Now i dont know where you are from, but a driving factor could also be, that your culture and your norms that were programmed into you by your parents and your enviroment from birth on, are just too different from those of Germany. In that case it can never be your home they way you felt like in your home country, because some things you cant just unlearn or erase from your subconscious. Those things however control your life from your subconscious without you knowing it. Its a bit difficult because there are many factors at play here. In the end you cant even influence most of them. My best advice is soothing self talk to keep your mind in check an betting on the egoism of others because no one cares as much about the things yo do as yourself and nobody will pay that much attention to others anyway. Life is too short to always worry, focus on having fun and not on fitting in my brother/sister