Construction costs are currently skyrocketing

There are quite different levers - for example, that municipalities are no longer obliged to sell properties at the current highest prices, the real estate transfer tax could be reduced, notary and broker fees could be scaled according to the investment amount, tax exemption of owner-occupied properties up to a certain price level, residency obligation,...

How exactly should the state intervene here? Just because it would supposedly subsidize apartments doesn’t mean they would be any cheaper; someone else just pays for it (alongside).

And the state can’t increase wages directly, except for its own employees—by exceeding union demands on its own ;) Otherwise, collective bargaining autonomy applies.

1. It doesn’t necessarily have to subsidize directly.
It could introduce certain relaxations in building regulations. Publish model/type plans that can always be built according to (even without an architect), reduce property transfer tax, prohibit construction obligations (either developer or general contractor—nothing disguised). Tighten antitrust supervision of building materials manufacturers/traders. Promote vocational training in crafts. There are certainly more things I can’t think of right now quickly.

2. Regularly adjust the minimum wage appropriately (which of course also leads to cost increases).

So it also lives additionally off state revenues, belongs to the poor church, and basically even received the land as a gift from the state.

In return, the municipality also received rights to allocate some apartments and can therefore manage social housing. And the rest of the residents so far only had precarious chances on the housing market; some of them now have their own apartment for the first time ever. It is easy to talk about social responsibility - but who is actually fulfilling it here?

Otherwise, I am also a great critic of the churches and their possessions - but here one really should keep things in perspective (pun intended)...

Point 2) These are, of course, the predestined homeowners! If we raise the minimum wage so much that even low-skilled workers can usually afford to build a little house, then our economy will not function sustainably.

I can't understand your thoughts at all. But I think you couldn't have known that these are mainly apartments for assisted living or for mentally disabled people. Nevertheless, completely normal apartments. The builder is a church institution that also operates workshops for these people.

And the church pays such prices for living space that it provides free of charge? I have not criticized the concept of social housing. I criticize that neighborhoods for low-income earners are being demolished everywhere and converted into luxury neighborhoods. As compensation, 10% of the apartments on the outskirts are then declared "social". Unfortunately, the residents who lived there before (and had to move away for 5 years) can no longer afford the new "social" apartments, even though the rent has only increased by 50%.

In the case of larger new company settlements, building company housing could also be made a condition... The pressure in the cities is also caused by the fact that companies like Microsoft, Google, or the large consulting firms pay very high salaries, offer attractive jobs but the municipalities hardly build. In Munich, Hamburg, and Frankfurt, it is now increasingly seen that two small terraced houses in older residential areas are being merged. This has already led to losses in housing space with the apartments. Now it is repeating in the area of small family houses.