Okay, okay, I HAVE to know how you connect Gamma and Omega to little planet. I may have misunderstood but I'm starving for your Robotnik lore because it's so, so good.
It's indirect; just that if you look at how R&D is done, imagine if you could time travel and just do R&D even faster. Let factories produce and automatically test themselves. Gather data. Go back in time. Redo it before you start, working off of the new data. Rinse and repeat. You could test new, bleeding edge, space-age materials this way, new ways of siphoning energy or generating it, etc etc. Eggman with a 300 IQ could easily go from his tech in Sonic 1 to making Metal Sonic in Sonic CD with that method, assuming he had enough time, against Sonic's own meddling.
So even if Eggman lost all the physical tech he developed on Little Planet after Sonic stopped him, undid his work in the past, and (presumably) made a Good Future, Eggman likely still has schematics and simple human experience after doing it all. Therefore, it'd explain why in Sonic Adventure, something like Gamma could even scrape anything close to being self-aware, and doubly so for Omega. It could be Eggman biting off way more than he can chew with what he's developed, since new machines could all be designed by him, but not anywhere close to being properly tested to know what he's gotten himself into.
He doesn't have access to easy time travel anymore, so he can't just do what he (presumably) did in CD. He has to, like any tech bro, now just move fast and break things in typical Eggman style. Hence, making someone like Omega of all people, who easily rebelled and ran off at the slightest annoyance. I'm sure there's holes to this theory, but many apply to just the nature of CD's time travel itself, I'd argue. We have to all just accept CD happened unless you like weird coma theories, and the implications of CD is very extensive if we assume Eggman retains his memories of the previous bad futures he tried to make.