The easy explanation for that is the social programs that care for the homeless are stronger in Germany. You don't see Berlin's homeless as a problem because they don't have to result to literally sleeping on the street. The people living in shelters are no less homeless, they just aren't as visible.
Usually, but not universally. Even when shelter space is available in a city like LA, it is not always easy to convince people to stay there. Lots of shelters have problems ranging from crime to forcing draconian rules onto the people staying there. In a place with a relatively comfortable climate like Los Angeles, some people legitimately prefer to be on the street. Their personal agency matters and we can't just round them up to throw them in a shelter. We need to improve the shelters until they are the obvious choice over the street.
It takes a certain legal regime, law enforcement regime, economic situation, climate, etc to make a place attractive to the homeless. I suppose that neither Vermont nor Texas have a lot of homeless people.
I also heard of the practice of buying a Greyhound bus ticket to the homeless and luring them to go to warmer, more abundant places, thus physically removing the problem.
Also it's usually noted that many US homeless would be in a mental institution elsewhere; they are not homeless by conscious choice to be anti-social.
[1] https://en.wikipedia.org/wiki/Homelessness_in_California
[2] https://worldpopulationreview.com/state-rankings/homeless-po...
Anyone who has ever walked around SF or LA and Berlin knows this implicitly. The US cooks the books.
https://www.feantsaresearch.org/download/germany241169298614...