Cartman's future being the only good in the bad timeline and the only bad in the good timeline mirrors the fact that in Season 2's "Spookyfish", Cartman's counterpart in the evil universe was good while everyone else was bad.
Why would Butters be referred to as Victor Chaos by the asylum director when his real name is Leopold Stotch? Well, after his parents abandoned him, he likely legally changed his name to Victor Chaos to distance himself from the family he realized never loved him.
Butters' job as a waiter (though soon to be manager) in the new timeline might also be a worthy accomplishment. Thanks to Randy's weed, the restaurant's customers would tip more generously and are more pleasant to deal with in general, so Butters has been able to make a decent living while doing something he enjoys. Butters seems especially suited to work with a job like waiting as he is polite, gregarious, enthusiastic, and would basically be hired to act as everyone's friend. Plus, he gets to use his sales talents without them resulting in violence and destruction.
Another reason that Butters might still be working as a waiter in a relatively later age than socially acceptable is because in the new timeline Cartman sabotaged his career, but he was finally able to advance back to success. That could explain why Butters is more unforgiving to Cartman than everyone else. Butters would have been one of Cartman's last holdouts for support until Cartman did something terrible enough to lose even that. Cartman's bad treatment of him would not only be stronger but also more recent than it had been for the others.
Healthcare advanced to the point where most of Timmy's disabilities were minimized, but Jimmy still stayed the same. Justified, as while Jimmy took a lot of pride in being disabled, Timmy hated it (even Season 17's "The Hobbit" showing him photoshopping his image to look like a normal boy) so it's likely he used the new medical advances to his advantage.
What really caused Butters' Sanity Slippage? As awful as his parents were to him, you'd think he'd be glad to be free from them. Well... in "Going Native" we leaned that Butters is a native Hawaiian (translation: white person who has a timeshare), and that they must return every few years to the land of their birth or they'll be consumed with rage. Thanks to the covid restrictions, he's been unable to make the trip for decades. It's no wonder he lost his mind.
In the new timeline Cartman doesn't meet Yentl and therefore doesn't change from his bigoted and jerkass self, becoming miserable and homeless as a result. Given that Kyle's kids resemble Cartman's, Kyle probably encountered Yentl first and married her thus preventing Cartman from meeting the one person that could change Cartman for the better.
Alternatively, Kyle could have ended up marrying Heidi Turner which would tie-in with the Aesop of Forgiveness, since it explains why Kyle was single and alone in the Bad Future possibly refusing to forgive Heidi for her actions as Cartman's Distaff Counterpart, while in the good future he's is married with kids suggesting that he has forgiven Heidi and wants to make their relationship work again, before eventually deciding to settle down with her.
Heidi Turner is briefly seen with her parents in the past. Given that this took place during "South ParQ Vaccination Special" where Bob White and the rest of Qanon were brainwashing children into supporting their beliefs, its very likely her parents are with Heidi to keep a close eye on her so she wouldn’t fall into any corrupting influences as she did with Cartman.
Cartman being homeless makes sense: it is possible Liane got sick of Cartman's behavior in adulthood, cut him off, wrote him out of her will, and kicked him out of the house. Considering how assertive she's become in later seasons, it would make sense Liane would get sick of Cartman if he became an abusive Manchild who leached off of her. The Season 25 episode "City People" and the "Streaming Wars" two-parter also hint at this, with Cartman costing his mother her job (and by extension, the house) out of selfishness; they are forced to move into an abandoned hotdog shack, and Liane's reaction to Cartman at the end of the former episode implies that she's already had enough of his behavior. Their bond is shown to be badly damaged at the end of the episode, and "The Streaming Wars" fully showcases just how fed up of Cartman's bullshit Liane is. Who's to say that she won't kick Cartman out as soon as she legally can?
While Cartman's fate is pitiable, it isn't too much of a shock. Cartman has the potential to be rich and successful, but his incredibly self-destructive pride means he inevitably ruins those opportunities.
In "Christian Rock Hard", for example, he manages to build a successful rock band with Token and Butters. But instead of being happy with his new career and grateful to his bandmates, he ruins the former and alienates the latter all because he can't win a bet against Kyle.
He manages to get a genuinely healthy relationship with Heidi, and he screws that up because his pride won't allow him to accept her genuinely good advice.
Cartman may have talent, but ultimately he squanders it with uncontrollable arrogance.
Whenever Cartman is trying to get something he always does it at the expense of those around him. At the end, in the good future, Butters claims that nothing could have changed the path he was on. We know that's not true, there is a possible future where he is happy and successful. It involves everyone else being miserable, thus only at the expense of nearly the whole world can Cartman get the future he wants.
