Gabriel's office in the older literature is consistent and narrow: he is sent to make something understood. In Daniel he is told to give the seer the meaning of the vision, and he is the first angel in the Hebrew Bible to be named while doing interpretive work rather than destroying or guarding.
Luke gives him the two annunciations, to Zechariah in the sanctuary and to Mary at Nazareth, and has him identify himself in words that became the standard formula for angelic authority: I am Gabriel, who stands in the presence of God. Zechariah doubts and is struck dumb; Mary questions and is answered. The difference between the two receptions has occupied commentators ever since.
In Islam the same figure carries the whole revelation. Jibril brings the Qur'an to Muhammad, is identified with the trustworthy spirit, and descends on the Night of Power. To Muslim readers Gabriel is not one angel among several but the channel through which scripture reached the world at all.
The lunar attribution used in the Western magical tables is a later fit rather than a source. It is a good fit: the Moon in the classical characters reflects rather than generates, and a messenger carries words that are not his own. But the fit was made by people arranging a table, and no ancient text about Gabriel assigns him a planet.
His feast was kept on 24 March in the older Roman calendar and was joined to Michael and Raphael on 29 September when that calendar was revised.