Okay, let's follow your advice and follow every easter egg as far as it can go. Rodin is called the eggman -- is he white? Does he have a crazy ginger moustache? Is he fat, into robotics, or even remotely interested in catching things that gotta go fast? Ezio makes fun of Rodin's baldness by making egg jokes about his head, and after that the reference falls apart as anything but a rude nickname.Cross referencing Easter eggs doesn't mean it exist in the same universe as Devil May Cry.
Bayonetta makes a ton of references from movies to video games. Sonic the Hedgehog, Viewtiful Joe, Okami, hell, there's even an easter egg from Jay and Silent Bob Strike Back.
If you're gonna count one little cross referencing Easter egg as "proof" of Dante's existence in Bayonetta's world then you can't ignore the others. If you do then just accept it for what it is. A cross referencing easter egg and nothing more. It's just because Kamiya worked on both. It's common for people to reference their own work in other projects.
- a character named eva is involved with "a legendary dark knight" as he saves earth from an invasion from hell
- Ezio Ferino is the name of dante's informant who points him to juicy demon slaying gigs; he has the same first and last name, occupation, physical description, and personality in both universes, and in bayonetta he repeatedly references his numerous other clients.
- Bayonetta summons not one, but three significant demons from the DMC universe. All 3 (Gigapede, Phantom, and Bael) appear phyiscally identical to their DMC counterparts, and two of them even have the same name.
- Dante was once a mercinary who adopted the name "Tony Redgrave" out of respect for "Antonio Redgrave", someone he knew personally. Antonio Redgrave is Luka's father.
The eggman joke is only a nickname, and immediately falls apart as anything more than a coincidental nickname the moment you look at it. All the DMC references are matching names, descriptions, sequences of events, and entire histories, all unusually specific, and none of them conflicting with established DMC lore at any point ever.
Not even remotely the same.