Found the text of the law.
https://www.scribd.com/document/580655753/Governor-Hochul-Conceal-Carry-Improvement-ActIt does not appear to include a definition of what constitutes "social media," so if I don't have Twitter, Facebook, Instagram, or LinkedIn, as far as I'm concerned I'm done.
... (iv) a list of former and current social media accounts of the applicant from the past three years to confirm the information regarding the applicants [sic] character and conduct as required in subparagraph (ii) of this paragraph; and ...
On the other hand, if you parse the language of that requirement, what it actually asks is only for a list of those accounts that confirm that you're a good person. So New Yorkers who want permits should all sign onto some sites that are all about gardening or car repair, make a few benign posts, and call it good.