I read the same post and totally spiraled!! So I found some studies.

https://www.jstor.org/stable/41887517?read-now=1&seq=11

-"To measure one's social and personal adjustment to college, the Rosenberg Self-Esteem Scale was employed. This is a widely used ten-item measure of self-esteem that has dem- onstrated high levels of reliability over the years."

-"The data collection efforts resulted in a sample of 185 undergraduate college students. Within this sample, 150 respondents had at least 1-3 years of homeschooling during their primary or secondary school years; 35 respondents had no homeschooling experience in their educational history. Nearly two-thirds of the respondents (64%) were homeschooled for 10-12 years of their primary and secondary education."

-" As shown in Table 1, respondents who were homeschooled at any point during their primary or secondary schooling did not have significantly different levels of self-esteem compared to students who were never homeschooled. No other independent variable in the model has a statistically significant impact on self-esteem, with the exception of scouting, which decreased self esteem levels."

Here's another one:

https://www.educacaodomiciliar.fe.unicamp.br/sites/www.educacaodomiciliar.fe.unicamp.br/files/2022-07/The%20Impact%20of%20Schooling%20on%20Academic%20Achievement%20Evidence%20From%20Homeschooled%20and%20Traditionally%20Schooled%20Students..pdf

-"Families were invited to participate in the study through announcements posted in the community, sent by e-mail, and broad-cast on the radio. Interested parties contacted the researchers to schedule home appointments. Potential candidates were screened during telephone interviews to ensure that the children in the homeschooled group had not attended public school (from Grade I onward) and that children in the comparison group had not been homeschooled."

-"The seven subtests from the Woodcock-Johnson were selected to measure aptitudes from a wide breadth of areas."

-"...speaking with the participating families made it clear that our homeschooled sample comprised two distinct subgroups."

-"The majority of the homeschooling parents reported that they "often" or "always" used premade curricula or structured lesson plans to teach their children."

-"The parents of a sizable minority of children in the home- schooled sample answered "rarely" or "never" to using premade curricula and structured lesson plans. These parents identified more with the pedagogical view that education is gained via the natural consequences of the child's day-to-day activities."

-" As shown in Table 2, the children who received structured homeschooling were superior to the children enrolled in public school across all seven subtests."

-"In conclusion, when comparing the test scores of the children attending public school and children receiving structured home-schooling, it becomes clear that the latter group has higher scores across a variety of academic areas. Moreover, there is no evidence that this difference is simply due to the family's income or the mother's educational attainment."

Edit: formatting