The definition of a rabbi for Judaism

peace,
The rabbi, as is well known, defines “Judaism” as nothing more than a commitment to Halacha. I do not disagree with this definition, and it even seems incredibly logical to me (since it is unique=particular), but it is not clear to me what the relationship is to a secular (?) Jew in this definition. In column 338 , the rabbi wrote in passing that according to this definition, secular people are also considered Jews because according to Halacha they are obligated to it, even though they do not recognize their obligation. Therefore, a Jew is not someone who is obligated to Halacha, but someone whom Halacha obliges.
This means that the secular person is defined as a Jew because the law, to which he is not declaratively and practically committed, claims his commitment to it by virtue of his origin.
This is difficult for me because of several reasons:
A. The Rabbi, in one of the books of the trilogy, argued that “compelled to perform a mitzvah” is only said of a mitzvah-observant who refrains from performing a particular mitzvah for some reason, but not of a person who declares that he is not obligated to the halakha at all. It is difficult to argue that there is religious value in an act done under compulsion, but there is no value in an act done by a person who is not out of a halakhic obligation. Just as we consider him a Jew because the halakha defines him as obligated to it, so we will consider his act a mitzvah, despite his non-obligation, because the halakha recognizes him as obligated.
on. If this is the definition of Judaism, it cannot be inferred from it that halakhic commitment is a necessary condition for conversion, as the rabbi claims. If we assume that there is some mechanism for conversion, then a gentile who has carried out that mechanism is considered a Jew and is obligated by halakhah, even if he does not recognize this obligation. The rabbi can of course argue that accepting the burden of the mitzvot is part of the mechanism, but I understood from the rabbi’s books and statements (I am not very knowledgeable in halakhah itself) that his opinion is not based on any sources but mainly on the definition of Judaism as a halakhic commitment, and if the rabbi wants to include secular people in this definition, then this certainly does not follow from the definition.
Although it must be admitted that even if my words were correct, it is very logical that accepting a halakhic commitment is a condition for conversion, and so on.
third. According to this definition, any religion in the world that claims our commitment to it, we inevitably enter under its wings. If Christianity, for example, claims that we are all obligated to believe in the divinity of Jesus Messiah, then we are all Christians in this sense. The rabbi claims that even secular people identify themselves as Jews because the halakha claims their commitment to it, even though they do not recognize the authority of the halakha to claim anything. This is exactly how we are Christians even though we do not recognize the authority of the church to claim anything. It is true that Christianity, and most religions in the world, do not have halakha in the Jewish legal sense, and even if they do, it is not the main thing, but there are binding principles of faith and they are the main thing of the religion, and therefore it is impossible to simply extrapolate from the rabbi’s definition of Judaism to the definition of Christianity or any other religion (especially in light of the rabbi’s well-known opinion on “binding principles of faith”). But nevertheless, I can invent a new and fundamentally halachic set of norms, and it will be called in Israel ‘Abrahamism’, according to which anyone whose last name begins with A is obligated to it (even if he does not recognize it) and then the rabbi, by that definition, is a distinguished Abrahamic.
The alternative to all this is to say that indeed the definition of Judaism is a commitment to the law and not to those whom the law obligates, which excludes from Judaism those who are not committed to it, the secularists. The law requires them to be Jews, but they choose not to obey it and in practice – not to be Jews (this is of course on the essential level of Judaism, which the rabbi claims exists, and not on the ethnic-cultural-national level).
But whether you accept the first or second formulation, and whether my words are valid or false and repulsive, I would like to ask whether the rabbi’s definition of Judaism is a halakhic or extra-halakhic decision, and in any case what halakhic and other implications does it have (apart from your position on the subject of conversion).
I apologize for the barbarity.