The Feast of the Month of Ivor

In honor of the Rabbi:
In the Sanhedrin (8:1), there are laws regarding a rebellious and apostate son: "He who eats in a group of mitzvahs, eats at the new moon, eats the second tithe in Jerusalem, eats the dead and the abominable and the unclean, (he eats the first tithe and the first tithe that was not accepted, and the second tithe and the holy offering that were not redeemed), he eats something that is a mitzvah… – he does not become a rebellious and apostate son." It is said in the Book of Genesis (ibid., 2b) that there is an addition to "something that is a mitzvah" – "for the consolation of the mourners," and Rashi explains, "The rabbis have established it in a certain way, but it is from the Rishi that we are a group of mitzvahs, we were priests who eat holy things or Passover." The difficulty is from the Rashi, and after all, even the feasts of the new moon are from the rabbis, and what is the number?
It is stated in the Megillah (28) that one does not eat, drink, or sleep in the synagogue, and likewise in the Talmud (28) that this is permissible. The Rishonim differed as to whether this is permissible in the Shofi or in the HaGa'ut Asheri (22:3) that this is permissible from the outset, since it is permissible in Jerusalem to eat the feast of the new moon in the synagogue. However, the Maimonides ruled (Tefila, 11:6) "And the wise and their disciples are permitted to eat and drink in the synagogue without delay," and the Tza'at is what is the answer to the view of the HaGa'ut.
Can the above two problems be resolved by saying that since there is no specific person responsible for the crossing of the month, the Ka'u'a is judged as if the kiddush of the month depends on him from a halakhic perspective ('the language of the scales'), similar to the law that when a fiqun is performed, even though ten people can help with it, the Ka'u'a is obligated and in any case his act delays Shabbat (Menachot, 64), and this would explain the Maimonides' explanation for the reasoning (in the context of kidduh) "is found to be a failure for the sake of the law" "even though these testimonies are useless, lest one of them in the future will have useful testimony in another month, and he will be prevented from coming to testify because his words were not heard in the past." Thus, the reality that there is no reliable testimony leads to the fact that any approach to kidduh constitutes an integral part of fulfilling the mitzvah. This distinction seemingly resolves both of the above-mentioned issues, as there is a fundamental difference between the feast of the new moon and other mitzvot. In the Rabbi's opinion, are these things correct from a halakhic/philosophical perspective?
thanks!