the court in the last 4 years has been 5-4 conservative. all major cases involving the ACA were
5-4, so having a 6-3 court would certainly jeapordize it. Obergefell was also
5-4 so that would be at risk, and alito and thomas recently said that it should be revisited.
this abortion restriction Louisiana put in place was only struck down 5-4. With Barrett on the Court it would have probably been upheld
https://www.supremecourt.gov/opinions/19pdf/18-1323_c07d.pdf
the following cases are from the Obama Admin. but because a 5-4 Court was still in place they are still relevant:
Shelby County v. Holder was a landmark case threatening voting rights from discrimination on the basis of race.
5-4 decision
Utah v. Strieff was 5-3 and threw the Fourth Amendment in the trash