Shabbat mode oven

Do the relievers have anything to rely on? Yes, I'm talking about a case where the thermostat apparently works after opening the door to reach the required temperature again.

Yes, but barely. This is a Risha Danichal ruling on the prohibition that I think is from the Torah but according to the majority of rabbis. Beyond that, I think there is room to see this as being busy and not not intending. You are busy opening the door, and at the same time something else is happening. As some rabbis wrote about someone who walks by a light sensor and activates it, that there is no such thing as not intending and being busy. He is not busy activating the sensor but walking. Of course, there is a division.

What about the fact that the oven is a dumbass?

A Sanhedrin was established and I didn't hear about it?!

Rabbi, why is it necessary for a Sanhedrin to be established for this? After all, if using an oven is indeed considered a normal way of cooking, why doesn't it fall under the definition of a cook as a cook?

Because this is a new decree. It urges to introduce a new situation under an existing decree. Like the argument of a ban on cycling, lest it come to a correction.

But the ruling is general for all cooking methods, isn't it? Why would a new situation that falls within the limits of the prohibition not be considered part of it? After all, if an oven had existed in their time, it would be quite simple for them to have been explicitly directed at it as well? Most, if not all, rulings, when there is no Sanhedrin, are word for word, right?
It's like if a new animal (that didn't exist in their time) were created that met the conditions of a pure animal, it would be considered pure, wouldn't it?

Thank you very much Rabbi for the answers.

There is a difference between the laws of the Torah and the laws of the Rabbis. In the Torah, a milita is compared to a milita more than in the Rabbis. Therefore, if a rule is not invalidated by a taste, it is by a khumarah and a kola. For example, no one would think of prohibiting soy foods like a tibbol with milk.

Regarding the signs of purity, this does not concern us at all. The signs themselves were given there and the entire application is left to us. It is not a matter of word-for-word analogy.

Regarding soy foods, it is not similar in my opinion, since the appearance of the raw material does not resemble meat at all. Moreover, the definition itself is specific to chicken and to something that looks like meat (fish is not included, for example). If a new type of chicken is now created that did not exist in their time, cooking/eating in milk should indeed be prohibited. No?

Regarding the signs of purity, I gave this as an example of a situation where once the conditions of the commandment/prohibition/decree are established, they are not limited to what existed at the time, but also "new" things, as long as they meet the criteria, will be subject to the prohibition.