Shaikhul-Islam Ibn ul-Taymiyyah rahimahullah:
“The gathering of the people for food on the Two Eids and the Days of Tashreeq is Sunnah. And it is from the signs of Islam which the Messenger of Allah sallallahu alayhi wa salam established as Sunnah”
[Majmoo’ al-Fatawa (25/289)]
While it might not necessary be a Sunnah per se, it is permissible to come together and eat on the Day of Eid as it is a good custom.
Faisal Ibn Abdul Qaadir Ibn Hassan