Federal and state refunds come from completely separate entities. There is no rule as to which one will come in first or how long it will be between their arrival in your account.
TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer. “21 days” is not a promise from TurboTax or the IRS.
First, check your e-file status to see if your return was accepted:
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 35a of your 2023 Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.
https://ttlc.intuit.com/questions/2580357-who-provides-the-refund-processing-service
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved