Bricks: Are differences in the thermal conductivity value of 0.03 noticeable?

Can you really feel the difference between 0.07 and 0.10 W/mKp in the house or is it rather negligible? Do I have to heat significantly more if I choose 0.1?

Thermal transmittance values are to be understood linearly, unlike sound levels, so your two comparison stones relate to each other by a ratio of 7:10 in this respect. Practically, heat transfer with the "better" stone takes ten hours to transfer as much as the other stone does in only seven hours. So it is not negligible, but noticeably significant in terms of calculation. However, you set your thermostats to target temperatures, not to loss quantities. So your heating bill will indeed be noticeably affected. Nonetheless, I would always prioritize my stone mantra over the heating bill.

I would always put my stone mantra above the heating bill.

I know this is a topic of its own and in my case it should be a red brick. Am I now totally off with, for example, an MZ10 with 0.1 and do I have to worry about keeping my house cozy warm in winter or having to sweat in summer?

Am I now completely off with, for example, an MZ10 with 0.1 and do I have to worry about keeping my house cozy warm in winter or sweating in summer?

Once again, so you finally understand. Every house will become cozy warm. Even if you install 0.30 bricks. You then "only" have to heat more. Understood? Oh yes, you have to achieve KfW55 anyway. And if your MZ10 is sufficient for that, you have a new building that complies with legal standards and is built thousands of times like that in Germany (to be understood as a complete package, not based on a single product like a brick).

Am I now totally off with, for example, an MZ10 with 0.1 and have to worry about keeping my house cozy warm in winter or sweating in summer?

"My" house is as old as I am, monolithic pumice caliber 300. You can endure it in every season. My annual statement says I am mostly around the average. Chill out and definitely don't plan your house with this focus. We don't even have the apartment partition walls made of sand-lime brick, and yet I don't hear the dog next door (in case that would be your next fear after checking off the heat transfer).

In your example, user behavior probably makes much more of a difference than the different types of stones.

In my opinion, a compelling argument that probably applies to every user. The now widely accepted mindset of high temperatures certainly increases consumption more than the choice of a particular material.
Of course, nobody should be cold, yet I often hear and read about almost indispensable assumptions regarding temperatures that cause more increases than could be prevented by construction.

I now live in a really well-insulated house (lower than Kfw40) and would never want it any other way, not only because of subsidies or possibly required standards. There are winter days when the heating doesn't run at all because the insulation keeps the heat inside.
Adding more insulation in some places and less in others makes no sense; there must be a consistent concept or the desire to insulate to the maximum. In my opinion, it also doesn't heat up as strongly in summer despite the south side as our old house (36 cm Poroton).
Certainly, this pays off, whether in resale value or heating costs, but it also currently provides a noticeable added value that would make it worth implementing for me.
So you should consider from the outset whether these circumstances are important to you and then consistently follow the path (floor slab, windows, wall insulation, roof insulation, etc.) or not; then the "normal" things your construction company does will be enough to get a house where you can live comfortably.
It has also become somewhat trendy to emphasize these values so much; what matters is the overall project.

If I have a photovoltaic system with storage

I would rather consider the storage as a "gimmick," even though I have one myself. I would definitely invest more in insulating the house. Maybe a few points can be found, and boom, the insulation might even be paid for.