What do our rabbis of blessed memory say about Shavuos, or any chag that celebrates the purposes of that chag as well as at the same time celebrates or renews a previous brit or similar? From shul I heard that Chag Shavuos is also a renewal of the Noachide Laws or the Covenant with Noah. I would like an authoritative source [rabbinic or pre-rabbinic].
And He gave to Noah and his sons a sign that there should not again be a flood on the earth. He set His bow in the cloud for a sign of the eternal covenant that there should not again be a flood on the earth to destroy it all the days of the earth.
For this reason it is ordained and written on the heavenly tables, that they should celebrate the feast of weeks in this month once a year, to renew the covenant every year.
Here is what one rabbi, Dr. Rabbi Norman Solomon, writes, in regards to Shavuos being "a renewal of Noah's eternal covenant",
"The Book of Jubilees, written before 150 BCE, provides the earliest and clearest hint. This book, now found in collections of Pseudepigrapha, is considered canonical by the Ethiopian Jews, Bete Israel, who call it by its Ge’ez name Mets’hafe Kufale (“Book of Division”). In Chapter 6 the author describes how Noah emerged from Ark on “the new moon of the third month” (i.e. Sivan) and, after making atonement by suitable offerings, established a new Covenant with God. This was to be an “eternal covenant,” and was observed by the Patriarchs but forgotten by their descendants until renewed at Mount Sinai: “One day in the year in this month they shall celebrate the festival. For it is the feast of weeks and the feast of first fruits” (6:21). Clearly, the author sees Mattan Torah itself as a renewal of Noah’s eternal covenant, and associated with Shavuot, though he stops short of actually renaming the festival."
As a side note, the book of Jubilees have been asked before at MiYodeya and according to @menachem,
Aryeh Kaplan "claims ... that the author [of the Book of Jubilees] was a firm believer in Talmudic Law ... And that R'Sadya Gaon had a hebrew version of the text."