As with every Yomtov other than Yom Kippur, the Second day of the Yomtov is for Messianic Noahides. The Teliya tells us that Messianic Noahides are to celebrate such days with a different emphasis from Judaism and in this case the focus for Messianic Noahides is supposed to be on the Ascension rather than on Harvest.
The first Shavuot was on the 6th of Sivan and commemorated the revelation of the Exodus 20:1-24:4 Constitution.
On the 7th day of Sivan HaShem feasted with the Sanhedrin.