KfW 55 or just the Energy Saving Ordinance - gas and preferably no ventilation?

You don’t need a chimney for gas, but a LAS (air/exhaust system commonly known as: chimney). This is not more difficult and only marginally more expensive than a pipe ventilation (wastewater) through the roof.

Thus, no major costs are to be expected here.

However, you need a gas connection + meter and this usually costs around 3 thousand or more depending on the supplier and distance etc.

ob wir nicht doch ein Haus, so wie früher bauen, also nicht so dicht,

Don’t get me wrong, but this statement is pure ignorance. No matter what kind of house you build especially if it is to meet the KFW requirements. It will be as tight as a plastic bag or poorly executed and then simply not so tight.

(was kostet es denn mehr mit Feuchtigkeitsrückgewinnung)

About 1000, but nowadays I wouldn’t want to build without moisture recovery.

hier Kfw55 hinzubekommen oder brauchen wir dazu die ST?

Only the energy consultant from the general contractor or an independent one can help you with that. The ST is of course the path of least resistance for everyone.

we cannot claim the KfW loan and also do not receive the extra 5000 grant.

This amount does not cover the additional expenses anyway, and is therefore just a bonus if you happen to plan KfW55-compliant measures anyway. I think aiming for the standard just because of the subsidy is nonsense. In my view, KfW55 offers from developers are primarily a sales argument with the message "already meeting a future standard today = creating higher value stability." The builder / homebuyer is supposed to have the romantic notion of paying off their little house faster because they would have to pay much less to the municipal utilities.

I do not follow this conclusion: the same control command can also be triggered by the hood being turned on.

Well, and where does the air that the extractor hood sucks out come from? That's why a connection to the window is correct.

Although somewhat off-topic: We are currently in the process of planning/buying an apartment. Energy Saving Ordinance 2014, no KFW with heat recovery. The developer says in this context that a recirculation system is completely sufficient and can possibly even be omitted because the system gets the necessary air.

Is that correct or all just nonsense?

Cooking fumes essentially consist of moisture, odors, and grease. These three components have to go somewhere. Moisture can be easily ventilated out by the ventilation system, odors may take longer than a fume extractor to be removed, but that’s not a problem; if that bothers you, you can simply open the window in the usual way. However, the grease cannot be ventilated out and will instead settle on various surfaces and become sticky if you don’t clean it off promptly. A (good) recirculation hood with its activated carbon filter also helps to reduce odors.

I will buy a recirculation hood; currently, we have an exhaust system and I find it incredibly annoying to always have to open the window (even at -20 degrees). However, I wouldn’t completely do without a fume extractor.

So far, we have been cooking without a range hood. Works great. After cooking, we just wipe over the surrounding cabinets. Eventually, there will be a proper one. So open the window and clean a bit, and that's it. That's why I would never give up my beloved ventilation.