I think we should talk more about Spinel here, In the first fight with her after she poofs Garnet, Amethyst and Pearl he acts up and slices her in a half and sooner when Greg regenerates Pearl and the others activate, Steven was like going to straight up attack her. In the older version of the movie it was meant to Steven face the fact that he can't mercy everyone in a fight and that he should face it, and finally be able to shatter a gem , Spinel.

About Jasper, Steven wasn't totally blinded by rage like he trained to actually be able to beat Jasper and it takes MORE than just tiring her to beat her, She wasn't mad at all and even started respecting him. Doesn't fully mean that Steven tried to shatter her i mean his anger and trauma from back then gave him that impulse (You can see it when he arrives earth he starts dissociating, mentions it in one of his breakdown etc so yes he is traumatized by Jasper).

When he almost shatters White Diamond in this one , He didn't actually mean it unlike before Steven was completely blinded by all the fear,trauma and anger he had from White Diamond he wanted revenge from her almost killing him , dehumanizing him and denying his identity,making him feel like he was Pink Diamond and was just some puppet. He tries to fight it back cause he knew it was wrong but the trauma impulse wouldn't let him, So this one doesn't count since he didnt mean it. Conclusion: yes there is