Only Where's My Refund can provide you with an accurate Direct Deposit date. Once your return was accepted by the IRS, they no long update TurboTax.
Processing simply means that the IRS is working on your return, it is the stage after accepted and before being approved, and the length of time this step take will vary from one return to the next. Here is more information on what's happening with your return
https://ttlc.intuit.com/replies/4689484
If you choose to have your TurboTax fee taken from your refund, that refund will be handled by Santa Barbara Tax Products Group (SBTPG):
Here is information about getting help with your refund that is being handled by Santa Barbara Tax Products Group:
https://ttlc.intuit.com/community/refunds/help/who-provides-pay-with-my-refund/00/26410
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