@PandasAreCute In terms of impact on admissions at tippy top schools:
A decent AIME score has about as much impact as submitting an STS paper;
Qualifying for USAMO has about the impact of being an STS semifinalist;
Making IMO team has about the impact of winning one of the top prize at the STS finals.
I wouldn’t say any of them “look a lot better” than a 4.0/1600, but if you already have a 4.0/1600, they certainly don’t hurt, and can be the difference - particularly USAMO/STS Semifinalist and above.