From the description of the bill law (bold added):

https://legislation.nysenate.gov/pdf/bills/2023/S7694A

To limit access to addictive feeds, this act will require social media companies to use commercially reasonable methods to determine user age. Regulations by the attorney general will provide guidance, but this flexible standard will be based on the totality of the circumstances, including the size, financial resources, and technical capabilities of a given social media company, and the costs and effectiveness of available age determination techniques for users of a given social media platform. For example, if a social media company is technically and financially capable of effectively determining the age of a user based on its existing data concerning that user, it may be commercially reasonable to present that as an age determination option to users. Although the legislature considered a statutory mandate for companies to respect automated browser or device signals whereby users can inform a covered operator that they are a covered minor, we determined that the attorney general would already have discretion to promulgate such a mandate through its rulemaking authority related to commercially reasonable and technologically feasible age determination methods. The legislature believes that such a mandate can be more effectively considered and tailored through that rulemaking process. Existing New York antidiscrimination laws and the attorney general's regulations will require, regardless, that social media companies provide a range of age verification methods all New Yorkers can use, and will not use age assurance methods that rely solely on biometrics or require government identification that many New Yorkers do not possess.

In other words: sites will have to figure it out and make sure that it's both effective and non-discriminatory, and the safe option would be for sites to treat everyone like children until proven otherwise.