Insulate house with 30cm wall?

A cost/benefit factor (payback) makes sense to me since WDSV is now viewed much more critically than it was a few years ago, I wanted to inquire about the current status in connection with the corresponding masonry. It is partly "shocking" when you read older contributions on this topic, when WDSV the thicker the better was! KfW55 is uninteresting to me, energy saving ordinance depending on the extension size as well.

I wanted to ask about the current status in connection with the corresponding masonry.

One can have different opinions about ETICS, but it is not specific to the type of stone, neither for desired nor for feared effects.

KfW55 is uninteresting to me, EnEV depending on the size of the extension as well.

Sort of. For the extension itself, the current standard will play a role, and at least as far as the same rooms are included old and new, I would consider a strong "gradient" of the U-values critical.

Financially, something like this probably only pays off for you late. The comfort aspect is also questionable. How skilled are you in craftsmanship for this?

I would say an ambitious hobby craftsman.

There is, for example, the possibility to insulate the façade itself with a curtain wall. This is a good way to solve it economically.