I don't think anything was required. He definitely could have chosen a different path to the nomination.
Reagan quote literally says the opposite of what you said about Reagan appointing Sandra Day Oconnor - he literally said he was selecting the most qualified woman. DId you look for what Reagan said at the time before you posted this?
A few months later, at a news conference in Los Angeles, he made it official, saying: “I am announcing today that one of the first Supreme Court vacancies in my administration will be filled by the most qualified woman I can possibly find. … It is time for a woman to sit among the highest jurists.”
https://www.washingtonpost.com/history/2022/01/26/biden-reagan-supreme-court/