Something I really appreciate about Mister Doctor Eggman is how he pays homage to western depictions of Eggman.
Most obviously, his goggles and toupee are based on Eggman's appearance in the first Sonic movie.
But if you analyze his appearance further there are also nods to Eggman's SatAM and AoStH designs. Firstly, he wears a full body spandex suit having a design that divides it into quarters, with red and black on opposing hemispheres and separated by a yellow line. However, Mister Doctor's colors are swapped so that black is on top, with red on the bottom. He also wears boots much like his DIC iterations. And his shoulder pads could be a nod to the ones worn by the doctor's SatAM incarnation (though obviously much more toned down, lol).
And the side of his suit even has a yellow cross further separating these colored sections, similarly to the one on the front of the old cartoon versions.
And maybe it's just me, but his thinner, floppier mustache also reminds me of SatAM Robotnik's mustache.
Beyond his appearance, there's also the fact that, like SatAM Robotnik, he's another version of the doctor who has successfully taken over, and resides in a giant egg shaped base situated in the center of a bleak, polluted city.
And much like older western depictions, Mister Doctor Eggman has been shown to convert animals into mechanized minions (which is itself a more twisted spin on the original badnik concept).
But all of this shouldn't be too surprising considering that the studio that created Sonic Prime, WildBrain, is basically the successor of DIC, the studio that made the old Sonic cartoons. And if early concept art is anything to go by, then they were originally going to be even more blatant with the references. lol