Semisegregation
Out of curiosity, I found government census and other demographic data for the area I live in, as well as for the schools in the area. The biggest variation in the data was the ratio between black and white students. (Note: this data is seemingly harder [in some cases, impossible?] to find for many private schools).

The extremes: Fuchs Mizrachi School is a modern orthodox Jewish private school. Gesu is a catholic school. Hawken school and University school are secular schools in a consortium of private schools. On the other side, there’s Shaw high school, which is in the next town over, East Cleveland, which is one of the poorest cities in America with 45.5% of children below the poverty line. Lutheran High School East is affiliated with the Lutheran Church–Missouri Synod (LCMS).
The demographics of the students in the public schools in Cleveland Heights – University Heights (ie. all of the public schools listed except “Shaw” and “Shaker Heights Middle”) doesn’t reflect the demographics of the city itself. Some of the difference is from kids going to religious schools, where certain demographics highly correlate with certain religious denominations. The other part of the difference is likely from people sending their kids to non-secular private schools where tuition can be up to $40k per year. Presumably, the people willing and able to send their kids to those private schools still skews strongly in demographic. What makes this particularly regressive is that Ohio lawmakers have made a voucher program that subsidizes up to $8.5k of that per student, by taking money away from the public school. Thus, the public schools suffer from lost funding, more people of means flee to private schools, on repeat; it’s essentially a positive feedback loop that destroys public education. Which further hurts already disadvantaged people; essentially another factor in the income inequality positive feedback loop we’re on. I really hate positive feedback loops.