According to an Interview this Beebo Saves Christmas Christmas Special is Supposed to feel like the Christmas Special that the Characters in The CW Arrowverse Once Watched like Kara Danvers/Supergirl and Sara Lance/White Canary and Ray Palmer/The Atom, etc...
The Very First Appearance of Beebo was in CW's DC's Legends Of Tomorrow Season 3 Episode titled 'Beebo The God Of War' which Consequently the Christmas Episode for that season of Dc's Legends Of Tomorrow and ever since then Beebo had at least one Appearance in every CW Arrowverse Show Up to this Point Excluding Batwoman. As a call back to his first Appearance on the for mentioned episode of DC Legends Of Tomorrow. Beebo even Appeared During the 'CW's Crisis On Infinite Earths' Crossover.