Spot on, there is a fantastic working paper that everyone should read.
https://www.nber.org/papers/w25315The paper evaluated US students who all got into the best unis (top 30) and compared lifetime earnings, marriage rates, advanced degree rates etc. between students who chose the best uni they got into versus those who chose a lower ranked one (by median SAT score) Importantly, they controlled for SAT score, GPA, parental income, and the schools the students got into. They found that for male students there were no differences between students who went to the best uni compared to a uni with SAT scores 100 points lower, roughly lets say the difference between an Ivy vs UCLA. Now keep in mind this was done in the late 70s and only applies to students at elite schools. For female students, there was a difference in favour of going to the elite school, but when excluding non-full time employees, the difference disappears. That is to say that choosing the elite school made you more likely to work full time, which is why lifetime earnings were higher at the elite schools (but this may no longer be the case in 2023 vs 1977). What the authors found was that for women, choosing to go to the elite school instead of the slightly less elite school, increased full time employment rates and advanced degree obtainment rates, slightly decreased marriage rates, but for those who did marry, they made more money. They theorize this is because for women in the 70s, those who choose to go to the elite school may have a smaller but more accomplished dating pool, which reduced marriage rates, but also allowed those who did get married to have improved incomes themselves. Whereas for men, the outcomes don't change because they are a more homogenous group, since men were expected to find employment and were broadly considered more desirable if they were able to do so.
So all in all, your school choice does not matter, if anything, differences in graduate outcomes are due to the students own characteristics rather than their choice of school. If two kids who both got into Harvard with similar SAT scores, GPA and parental income, athlete status etc (among others), if one chose Harvard and the other chose UCLA, their lifetime earnings were essentially no different.