External books

Does this mean that the commandment, “Observe the month of spring and celebrate Passover to your God, for in the month of spring the Lord your God brought you out of Egypt by night” proves that the calendar is lunar and not solar?

Thank you very much.

Indeed. If indeed this is the intention of this mitzvah (to the past to ensure that Pesach falls in the spring).

And yet (sorry for the digging)
The translation was done before Chazal by the best of the sages at that time. Before there were disputes, it seemed that it was supposed to be a definitive thing!
It seems as if something is being hidden (reading in external books was forbidden). ”On the eighth of Tevet, the Torah was written in the days of King Ptolemy in Greek, and darkness came upon the world for three days”. (Language of the Fasting Scroll)

Who said this was before the disputes? It is more likely in my opinion that the translators belonged to the same faction and the Sages rejected the translation and saw it as darkness, and therefore established three days of fasting.

If so, then why was it so important that a miracle be performed and everyone wrote the same thing? After all, the matters were already in dispute.

The description that there was a miracle is a description of the Talmud. It is not certain that anything supernatural really happened there. It is possible that everyone simply thought a similar and righteous thought. Incidentally, who said that if they disagreed with the sages, the Holy One was not with them? Either because they were right or because even those who are not right are "these and those are the words of the living God."