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It isn't Unintentionally Unsympathetic, you are correct. As you said, it is much closer to Easily Forgiven.
Well, (and this is me speaking without much knowledge of the show itself), Easily Forgiven seems to expect the audience to forgive the villain, too- they're redeemable and misunderstood, rather than out-and-out evil and worthy of in-universe and out-of-universe hatred. That seems to be the situation here; their traits as villains made them so unsympathetic to some people, that the show expecting them to just forgive them comes off as expecting them to like and sympathize with them despite their evil.
Or look at it this way: If a villain ends up being redeemed, the work usually tries to build up to that and make the characters seem sympathetic enough to change at some point, even if they're incredibly flawed. So if a work just gives us incredibly evil-seeming characters and fails to convince us beforehand that they're not pure evil, that retroactively makes it seem like we were meant to sympathize with these characters from the get-go, and that the work simply failed to make them...well...sympathetic.
My point in all of this is that I'm not sure this should be considered a shoehorn just because it's discussing the acts they did before redemption, because the worse a character acts before redemption can change how much the audience is willing to sympathize with them after redemption, even if they're suddenly acting completely differently.
However, I'm not a huge SU fan, so I couldn't tell you how accurate the example is. This is just my two-cents on the whole "unsympathetic before redemption" issue.
Working on: Author Appeal | Sandbox | Troper WallHaving seen it, I wouldn't say that anyone is expected to forgive them. Steven himself has a sceptical look on his face as they act like loving parents/grandparents. He also can't wait to get back to the people who raised him on Earth instead of staying with the diamonds.
I've seen several analysis videos that point out that the only reason the diamonds listened to Steven was because of his connection to Pink Diamond and that Steven simply took advantage of that to reform homeworld. White Diamond is at best shown as a racist grandma who continuously gets corrected by the grandchild everyone knows she wants to like her.
Edit: Then again, the opinion on Unintentionally Unsympathetic is also popular. If anything I'd suggest putting it on Broken Base or something similar.
Edited by Meppe

UnintentionallyUnsympathetic.Western Animation
I toned down some of complaining, but I question if it's an example given it's a notoriously controversial issue. I believe it's misused (at least as written) as this trope must explain why they were supposed to be seen as sympathetic despite the circumstances . Those traits are why they were supposed be be unsympathetic as villain until they begin to redeem themselves. It's just complaining about being Easily Forgiven. From my limited understanding of the series it sounds like it exaggerating their negative personality traits.
I've asked
Unintentionally Unsympathetic cleanup but it's been inactive for the last few days and this looks like a big contentious issue.
Edited by Ferot_Dreadnaught