Biden has not been socially liberal. He’s been an establishment Democrat his whole career. He has trailed the left and towed the line of the party, but he has patently not been socially liberal. However, he has atleast brought on policy advisors who are socially liberal like Heather Boushey, Stef Feldman, and Brian Deese.

Here are some links for reference.

https://www.vox.com/policy-and-politics/2019/6/20/18677998/joe-biden-1994-crime-bill-law-mass-incarceration

https://www.nytimes.com/2023/03/09/us/politics/biden-centrist.html

https://www.cnn.com/2021/04/11/opinions/biden-budget-proposal-centrism-ghitis/index.html

https://www.nytimes.com/2020/10/29/us/politics/joe-biden-advisers.html