My Federal tax was accepted on Saturday 2/13 it seems like my ny state is still pending after being sent to irs

The IRS just began accepting/rejecting 2020 returns on Friday, February 12, 2021.  You need to watch your emails for the acceptance/rejection notice that may take until mid-February or later to arrive.   And watch your spam folder too.   There are a LOT of e-files on servers so it may be several days after the IRS opens before you get an email.  There are so many returns waiting —kind of like trying to put the ocean through a garden hose.  

When you e-file your federal return you will receive two emails from TurboTax.  The first one will say that your return was submitted.  The second email will tell you if your federal return was accepted or rejected.  If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.

A state return cannot be accepted until the federal return has been accepted.  And it is very common for it to take an extra day or more for the state return to be accepted.