Singular and plural – Halacha as plural?

Hello Rabbi,
I have looked into the singular and plural rule as well as the plural, but I have not found anything clear on this issue. I will briefly write my findings and would appreciate the Rabbi’s response, especially if you have proof here and there (from the Tanai-Amoraic sources).
Some believed (Mishpatim Yasharim, Peri Hadash) that this rule is the law from the Torah “after many have been persuaded”, and therefore applies only in face-to-face negotiations and by a majority, such as in the Sanhedrin. Others (Radbaz, Shach) believed that this is a rule from the Torah but extended it to the dispute of the poskim even though there is no negotiation, etc., and some believed (Rashba, Rama) that this is an independent rule that does not originate from the verse.
In my understanding, the more plausible opinion is the third option. The rule was created because there was no single Torah center and there was a lot of controversy, and therefore there was a need for many rules of jurisprudence. Here are some proofs:
It is impossible to deny the great differences between the Sanhedrin (Rubah Daita Kaman) and the dispute of the jurists (Rubah Dalita Kaman) – there is no hearing of arguments, no discussion in the act, it is difficult to name the dissenters.
Furthermore, we found many rules that conflict with this law, and this does not fit the nature of Torah law (and especially in a court of law where the majority always decides), such as the rules: Halacha as Beit Hillel, Halacha as Dibrei HaMekkel in Abel, Halacha as Rav in Issuri, and many many more (and it is difficult to say that they are all only in the rabbis). The exception is also made explicit in the Gemara (Ezra 7:1): “In the case of the Halacha as Rabbi Yehoshua ben Korcha – Ishtarich, the sd. Amina single and multiple Halacha as multiple, ka means that the Halacha as single.” And the Gett simply showed (beginning of Rule 5) that in several places in Shas they ruled as single. The Gemara is also known for the place of Rabbi Eliezer, etc., who acted according to his opinion against the multiple.
And I also saw that Rabbi Brandes proved from the language of the Tosefta in Berakhot (4:15) that Rabbi Akiva said that the halakha was based on the majority when there was no minyan regarding the matter in dispute and that this is also a new way of formulating the following of the majority (the halakha was based on the majority versus the majority to deviate).
Conclusion – This rule is not from the Torah, has many exceptions, and is difficult to apply (since it is difficult to count, and it is difficult to decide whether to follow a majority of the quorum or wisdom, etc., and what to do when the majority is not of the same opinion). In any case, it is said that this is a rule of thumb intended for situations of doubt, and apparently this is how the Rema understood and ruled (Homim 25:2, and its source is in Rashba 1:3), who wrote that it is one of the rules of case law for those who are uncertain about the law and are not fully qualified to decide based on evidence.
Of course, there is no need to mention that in practice, the judges throughout the generations did not always rule in the majority…
[And even more so, the Shach wrote (Homo 60, 120), who, as stated, believed that the rule is from Torah, and yet he wrote: “But what can I do if the words of Maimonides are essential and necessary in Shas, and the evidence of the Tosafot and the poskim who reached him for Fad are not evidence, and as I will explain, and it is a sin not to follow the majority of poskim in a place where it seems to the eyes of Shas that the law is with the few, and in particular because the poskim did not rule so except on the strength of their evidence, and since the matter is hidden, the construction falls.” And so does Rabbi Asher Weiss: “And it seems clear from this, that indeed it seems that even if the Torah says that the law is according to the majority, this is not the exclusive foundation on which the rule of law rests, and indeed even if they deviate from the majority to incline them in favor of the majority, since they have different powers that are superior to the majority, such as witnesses, financial power, to one side of the majority and the relative is inferior to the relative (see 22:23b), and their blood is like that in favor of the majority, even the law of the Torah has different powers in terms of the power of evidence and force, and therefore it is not surprising that this will be the case even in favor of the majority in deciding the law, and indeed even in the above case, they have different methods in favor of the majority against the majority of the majority. And I have already said in the MKA that knowing the truth is better than all the evidence in the world, and he who knows for himself, whether verbally or in writing, is not obligated to act according to witnesses or according to a majority, but according to his immediate knowledge, and therefore it is within the power of the Amoraim to determine a law as unique when they have ruled by the power of their Torah, whose reasons are clear to them as unique, since this is clear to them by the power of their Torah and the depth of their holy knowledge, and they are well-versed in this.”]
Bottom line – How does the Rabbi understand this rule? From Torah or Rabbinic? Also in the dispute between the Poskim? For situations of doubt or certainty? And what are the proofs?
Thank you very much!! (Also about the fascinating and waiting website…)