Ironically despite Shadow being mandated/localized to be a lot more antagonistic than he was before, he's had a terrible relationship with Dr. Eggman since around the 2010's.

You'd think they'd use Shadow's new personality as an excuse to be more directly affiliated with Eggman but now Shadow wants nothing to do with the guy. And that's so weird to me.

That's not to say I want Shadow to be a bad guy, but I liked how in past games, Shadow and Eggman had some respect for each other and weren't really enemies unless Eggman was directly threatening the planet Shadow swore to protect. If Eggman wasn't on the offensive, Shadow wouldn't go out of his way to attack the guy, probably in part due to Eggman being a relative of Gerald's and Maria's, and another part due to Shadow potentially seeing Eggman as a valued equal instead of as an annoying nuisance or an unsafe threat.

Shadow would always refer to Eggman by his title, "the doctor", not unlike how he referred to Gerald as "the professor". Everyone else calls him dumb nicknames and doesn't take him seriously, but Shadow's more courteous to him than that. Eggman clearly holds Shadow in high regard as well, and doesn't get pissy whenever he shows up the way he's always annoyed at Sonic. Maybe mildly annoyed on occasion, but he won't throw his signature tantrums over it.

Shadow breaks through Eggman's ceiling for an interrogation in '06 and all they do is have a casual chat about Mephiles before Shadow leaves. It's not friendly, but you don't get the sense that Shadow's ready to blow him up for no reason or that Eggman's ready to sick a bunch of mechs on him at a moment's notice. Shadow just gets what he came for, with Eggman attempting to sneak in a personal favor for good measure, and they both move on.

Eggman trusts Shadow enough in the Rivals games to fill him in on Eggman Nega's plans and ask for his help, and Shadow understands the stakes enough to not even try to object to Eggman's requests. He's all in right away. All he heard at first was that Eggman needed his help and Shadow was ready to give him the benefit of the doubt with only a vague distress signal to go off. Shadow also extends this confidence towards Metal Sonic, who everyone else sees as Eggman's tool (including Eggman), but who Shadow unconditionally treats like an individual.

They have a distant relationship in Sonic X and Shadow eventually takes his own path during Season 3's Metarex invasion, but not without leaving a Chaos Emerald for Eggman as he leaves because Shadow felt Eggman was at least owed that much. There's nothing deep or sentimental about the gesture, Shadow just felt like it was a reasonable thing to do.

I don't know, when you compare all this to IDW where every appearance by Shadow has him foaming at the mouth at every opportunity to kill Eggman, or Team Sonic Racing where Shadow is offended that he'd ever be accused of working with Eggman... it feels like something was lost along the way. In theory they aren't necessarily bad moments in the sense that Shadow's explicitly on the heroes' side in both cases, but it's jarring to see him be so dismissive or vengeful towards Eggman specifically. He used to not care nearly as much and because the franchise is so keen on making him one-dimensional, it never bothers to give Shadow any reason as to why he's been so sour towards Eggman in recent years.

Maybe I'm just overthinking it and Shadow's history with Eggman isn't something a lot of his fans take to heart. I don't see it getting discussed nearly as often as Shadow's explicitly heroic qualities. But I think this neutral relationship with the series' main antagonist helped Shadow be just as interesting as the other stuff that made him cool in his peak. The fact that despite being a hero, that doesn't mean he's just as much of an enemy to Eggman as the rest of the cast. Shadow keeping distant, but pragmatic connections with both the heroes and the villains was something neat that helped him stand out in the past.