A few points:
- The “Common” in Common Era refers to the ‘commonly used’ dating scheme, which counts years before and after the purported birth of Jesus in… 0? 1? Whatever. I think most Christian scholars agree that wasn’t the real date anyhow. That would be as opposed to the Jewish year of 5775 AM (Anno Mundi = since Creation) or the Islamic or Mayan or Chinese date or what have you. It should be rather obvious why Jews would avoid the term AD = Anno Domini = Year of our Lord.
- FYI, Ben Sirah is what Catholics call “Sirach”
So, what exactly is your question about the Great Assembly, anyway? We believe they decided which books would be canonized within the first century after the construction of the Second Temple and their decision was binding on all Jews, and the record of their rulings is faithfully preserved by rabbinic Jews. However, note that it would seem that the Sadducees, Karaites and several other breakaway sects have the same or very similar canon. Whether or not the canon was officially “closed” so early is open to debate. At some point before the destruction of the Temple, it was decided that there are 24 books and no more. Chanukah is a non sequitur as its celebration was instituted by the Rabbis and we admit it is not rooted in Scripture. It is referenced and explained in Tractate Shabbat of the Babylonian Talmud. The Book of Maccabees is non canonical.
The Great Assembly was a historical phenomenon after the return of the Jews to the land of Israel after the Babylonian exile. It is a special instance of the Sanhedrin, which is usually composed of 71 of the greatest sages and whose existence lasted until the Romans dispersed it during the 4th century CE (no offense, guys).
Jamnia, which is a city in Israel known to Jews as Yavneh, was the purported site of a council that canonized the bible. This is a theory propounded by a non-orthodox Jewish historian in the 19th century, not a traditional Jewish belief. Wikipedia:
“The Council of Jamnia, presumably held in Yavneh, was a hypothetical late 1st-century council at which the canon of the Hebrew Bible was alleged to have been finalized. First proposed by Heinrich Graetz in 1871, this theory was popular for much of the twentieth century. However, it was increasingly questioned from the 1960s onward and the theory has been largely discredited.”