I don't think Robotnik ever saw Stone's affection as genuine. He's used to people only valuing him if he's useful. His own bosses call him a freak, yet they put up with him because of his "perfect operation record". He isn't even shocked when he learns the goverment erased him, he expected it and had a contingency plan ready.
He keeps calling Stone a sycophant and a barnacle, because why else would someone stay with him if not to gain something? Clearly, Stone is just a suck-up wanting to ride his coattails. And Ivo is fine with that! He gets his ego stroked and in return Stone gets a slice of the world-domination pie. Mutually beneficial!
This symbiotic relationship gives Ivo a sense of control and ensures that Stone won't abandon him like everyone else. It also keeps him detached: of course Stone waited months or him to return from space, that's his job. His admiration is inevitable, and meaningless.
Ivo develops a genuine, irrational attachment to Stone, one he's able to rationalize as just being transactional. Those emotional walls shield him from the fear of abandonment that comes with caring for another person.
Except...even after Robotnik becomes a liability, Stone stays. There's no benefit, no plans of ruling humanity, not even a paycheck. Yet despite everything, Ivo tries to keep the old boss/employee dynamic going. He can't fathom the idea that someone would stay for anything other than convenience.
Then Gerald shows up, and for the first time Ivo allows himself to put down those walls. As an orphan he had built up this idealized image of family that he thought he could never have. People will use you then toss you aside when convenient, but family? Family is different. Family will always be there for you and love you no matter what. Family won't abandon you.
And suddently Stone's grovelling is no longer necessary. Why would he need someone who just pretends to like him when he now has all the unconditional love he's always longed for? That's obviously why Stone got so jealous, it couldn't have been real concern, he was just afraid of losing his comfy position as the lapdog of humanity's new king. Between a sycophant and family, the choice felt obvious.
And, of course, Gerald turns out to be just like everyone else in Ivo's life: just another person trying to get something from him. The second he stopped being useful, he was tossed aside.
His image of family is once again shattered, but those emotional walls are already down. Now that Ivo experienced that betrayal he was so afraid of, now that he's about to die, he's finally able to be honest with himself.
Looking down on Earth, he realizes there had only ever been one person on that blue marble who actually cared. Someone who had always been there, even when there was nothing to gain. Stone had never abandoned him.
But he had abandoned Stone. He tossed him aside, just like Gerald did to him. Now that he's able to understand how Stone felt, this is his last chance to make things right.
In his final moments, with nothing to fear, Robotnik puts down his emotional walls and opens up as best as he can. Stone had done so much for him, asked for nothing in return, and now it was his turn to do the same. Ivo helped save the world, not for recognition or convenience, but simply out of love.
Stone had always been a sycophant to him, yes, but he had also been a friend. A sycofriend.
