Berkeley is probably one of the more analogous examples to what will happen after the Supreme Court affirmative action decision.
It still technically allows race to be mentioned in the college essay, but California's Proposition 209 banned race-based affirmative action. A University of California study found that Berkeley saw a 60% decline in Hispanic, African American, and Native American enrollment after Prop 209. The applicant pool also shifted to higher income students at Berkeley.
After Prop 209, the underrepresented groups tended to enroll in measurably less advantageous universities, which led to worse long-run outcomes, particularly among Hispanic students. They saw declines in STEM program persistence, degree attainment, and wages.
The same study found that the barely rejected students that largely replaced the minority students after Prop 209, generally had similar long-run outcomes to the barely admitted students at Berkeley. That suggests that affirmative action had minimal negative effects on other students. In particular, Asian and White students saw no measurable change in long-run outcomes after Prop 209.
The University of California system adopted several race-neutral admissions schemes after Prop 209 to increase disadvantaged students' representation including guaranteed admission for a top percentage of the class and holistic review. These schemes increased enrollment of underrepresented groups, but not to the degree of affirmative action.