Construction costs are currently skyrocketing

We don’t have that, since the user I referred to also described the full-day number.
And unfortunately, it’s not "normal" either; in my circle of acquaintances, we pay by far the most, even in the middle of Stuttgart one of them pays "only" 350 for full-day care.
It is simply determined at the municipal level, the priorities of the community/city decide this.

In our district, 80% of the crèches offer full-day care. This costs, as far as I can see, about 10% less to the same amount as a comparable daycare spot.

Crèches or daycares with such short opening hours will gradually become fewer and fewer. If the daycare is "only" open 30 hours per week, then as an employer you can only offer your educators part-time positions. And just like that, you become unattractive again and lose out in recruiting, watching as the educators go to neighboring daycares because they get more hours there. In rural areas this is not yet so bad, but even here the number of applications in this sector is declining significantly and positions remain unfilled. In metropolitan areas like Munich, educators can choose their job and basically negotiate their salary freely, including bonuses and allowances.

On the subject of daycare costs: with us, a full-time crèche place, Monday to Friday from 7:00 a.m. to 4:30 p.m., including breakfast, lunch, and afternoon snack, costs 200 euros. Of this, you directly receive 100 euros back from the Free State of Bavaria as a subsidy, leaving 100 euros as your own contribution.

But it also depends on income, at least here. Maybe you simply earn better than others?

Apart from the fact that, for example, the Stuttgart buddy from my example earns significantly more than I do, there is actually only one "income rule" in our community. Want to have a chuckle? Gladly: with a household income (!) of under 27,500 per year, there is a 10% discount........... ;)

On the topic of daycare costs: For us, a full-time nursery place, Monday to Friday from 7:00 to 16:30 including breakfast, lunch, and afternoon snack, costs 200 euros. You get 100 euros of this directly back from the Free State of Bavaria as a subsidy, leaving 100 euros as your own contribution.

That is exactly what I meant. I have no problem spending money here, but these differences are simply so significant that they affect the fundamental decision of whether to send the child to daycare or not to work.
To it is a 500 euro net difference for us, that simply should not be.

We have 2 children, daycare and kindergarten both full from 7:30-16:30. Currently, we pay 680 euros per month, 50% of which is covered by my wife's boss. Her university colleague who stayed in Berlin pays 0 euros for 2 children..

However, I definitely would not earn as much in Berlin as here in BW. Everything has its pros and cons.

But hardly the Berlin Senate pays that, without the Länderfinanzausgleich it would be bankrupt. That is probably paid primarily by the Swabians and Bavarians*. Who then have to charge fees for daycare centers at home...

*The largest recipient of payments from the Länderfinanzausgleich in 2021 was, according to preliminary figures, the state of Berlin with around 3.6 billion euros. With a budget of 31 billion euros for 2021 and new debt of 7.3 billion euros in the double budget for 2020 and 2021. Incidentally, the largest donor in the Länderfinanzausgleich was the state of Bavaria with around nine billion euros...

Those who then have to impose fees on the daycare centers at home...

That is complete nonsense! It is solely up to the federal states whether and how much daycare fees they want to charge. It is also a question of mentality whether and when I send a child to daycare / nursery. In Bavaria, we have already had to listen to quite a bit about how one can even send children to daycare. :)

Stop bashing the federal states. Put your federal state government under pressure to make it free of charge.