Obligation of a mitzvah for someone who grew up in a secular environment

The question is whether a commitment is binding on a community even after several generations have abandoned it. For example, suppose that a community in the community committed to following a certain rabbinic authority and at some point the majority of the community members adopted another rabbinic authority (this is apparently the case with Yemenite Jews, some of whom switched from the Rambam to the Shulchan Arutz Sheva), do they all have to return to the first rabbinic authority?

Simply put, yes, but in any case, that is not the case here.
Beyond that, adopting a judge is not a commitment but a custom or at most a vow. It is a commitment to someone (a contract). And a contract is binding even if it was abandoned in the middle of a crime.

Does the acceptance of the public mean that God requires every Jew to act according to the acceptance of his ancestors and the acceptance is the case for a mitzvah like the commandment of firstfruits for those who have fruits, or is it an independent interpretation like the law of jurisprudence? The truth is that I am not sure that in your opinion there is a sharp difference between the two, (and still, as an independent interpretation, the acceptance of the public is about as interesting as a young woman from a haystack, of course).

I really don't see a sharp difference. The Torah was given to the public and the contract was signed with them, so it is reasonable to assume that it is the public that determines how it is carried out.

The question is, however, is the explanation a consideration of God, and because of it He now commands all kinds of commandments, or is it a consideration of each Jew for himself?

I didn't understand the question.

It is written in the Gemara that one must sleep in a sukkah. Is it now that at the end of the account, God Almighty directly commands me, “You must sleep in a sukkah” and He chose to command me this commandment and not another commandment because that is what was concluded in the Gemara that the public accepted (and if the Gemara had reached a different conclusion, or the public had accepted a different book, then God Almighty would have commanded me a different commandment). Or did God Almighty command only the Torah and now a person alone thinks that it is right and proper to obey the consent of the public just as it is right and proper to obey the commandments of God Almighty. If in your opinion this difference is not defined, perhaps you can explain why. For example, for someone like me, if there is a specific will of God, then it is something of importance even without me being interested in His considerations for will and command, but if it is an independent explanation (as I think about morality) then I certainly judge the reasonableness of the considerations.

What a person thinks “alone” is also valid by virtue of the will of God. Like morality. If I think that it is God’s will that I not sleep in the sukkah, then I probably will not sleep, according to both possibilities. But this is quite hypothetical because I have no real way of knowing this.
In short, God expects us to obey the interpretation that has been accepted into the law, even if it does not fit His original will. But that is as long as I have no other information. If in some way it is clear to me that this is a mistake, then we have entered into a judgment of wrongdoing in the commandment to listen to the words of the sages. There is room for discussion here.