This isn't for you as you do plenty but incase others read this, but if you happen to ever see a thick coat in a charity shop, second hand store, or thrift store (whatever you call it) and it is quite cheap, do buy it as there are many charities that take them to give to homeless people.
This is such an uneducated and entitled comment just showing how little regular people know about this situation in Germany. Its also one of the most commonly used arguments on this topic and its simply not true. Homeless shelters are overcrowded and extremely unhygienic. Our infrastructure isn't made for an ever-growing amount of homeless people. Law, rights and reality sadly grow appart heavily. "Die Tafel" is completely overwhelmed too. This statement might have been true 15 years ago but you should re-educate yourself on the topic.
It's not just the hygiene. it's that in those shelters you're constantly surrounded by a few mentally ill and possibly violent people who will lash out in unpredictable ways and make life worse for everyone with their constant tics and noises making you live in constant anxiety.
If you're homeless but not mentally ill yet, then being in such an environment everyday will definitely negatively affect your sanity as your daily struggle becomes surviving the shelter, instead of working to getting back on your feet. Kind of like being locked up in a prison but from which you can leave.
So then no wonder a lot of homeless people feel safer and less stressed just living and sleeping in public areas than in shelters.
They are usually not full either. However they have a strict no drugs, no alcohol, and no fighting policy. That means a lot of people aren’t interested in going to them.