Not sure what you mean by "scheduled" date. The date you saw from TurboTax is only an estimate. The IRS is in control of when your refund is issued. If you chose refund processing then the refund will go first to the third party bank. They take out your fees and send you the rest of your refund. That can take a couple of extra days.
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 2021 Form 1040) of your federal refund to track your Federal refund:
Your tax refund is not sent to TurboTax. TurboTax does not handle your refund at all.
Santa Barbara Tax Products Group, LLC (SBTPG) is the bank that handles the Refund Processing Service when you choose to have your TurboTax fees deducted from your refund. This option also has an additional charge from the bank that processes the transaction.
You can contact them SBTPG, toll-free, at 1-877-908-7228 or go to their secure website www.sbtpg.com
https://ttlc.intuit.com/questions/2580357-who-provides-the-refund-processing-service
No, there is no delay with your refund when choosing to pay your TurboTax fees with your tax refund.
Please see Where's My Refund? for additional information.