What happened.?

Did you choose to have your TurboTax fees deducted from your federal refund?  Is your refund taking an unusually long time to arrive?  Or was your refund seized to pay a debt you owed? if so, you signed an agreement that says TT can withdraw its fees from your account.  TurboTax would have sent several emails to you before they took the money out of your account.

https://ttlc.intuit.com/questions/1901364-why-was-my-bank-account-auto-debited-for-turbotax-fees

Turbo Tax says......

We understand that these are unprecedented times and we’re committed to helping our customers who are experiencing hardships. If you’re in need of assistance, call us by the Tuesday prior to your debit date at 1-888-808-1723 to speak with a trained specialist and mention “auto-debit”, or visit TurboTax Support.

As for your refund:

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.   Many refunds are taking longer during the pandemic.  The IRS is backlogged —-they are still trying to process millions of 2019 returns; they received millions of e-filed on the day they opened for 2020 returns, and now they are burdened with sending out another round of stimulus checks.   

Some delays are resulting from incorrect amounts that folks entered for stimulus checks they received.   Many people have been confused by the recovery rebate credit and completed it incorrectly.  The IRS may delay your refund while they cross-check to see what you received.  Some refunds are delayed because of the tax law changes that went into effect recently.   If your return has unemployment or the premium tax credit on it, that may be delaying it.

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 34of your 2020 Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

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://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

https://ttlc.intuit.com/questions/2724106-my-return-is-accepted-but-still-not-approved-is-there-a-problem-should-i-be-worried

From this IRS website - https://www.irs.gov/newsroom/irs-operations-during-covid-19-mission-critical-functions-continue

As of May 15, 2021, we had 300,000 individual tax returns received prior to 2021 in the processing pipeline. Including current year returns, as of May 15, 2021, we had 16.4 million unprocessed individual returns in the pipeline. Unprocessed returns include those requiring correction to the Recovery Rebate Credit amount or validation of 2019 income used to figure the Earned Income Tax Credit (EITC) and Additional Child Tax Credit (ACTC). This work does not require us to correspond with taxpayers but does require special handling by an IRS employee so, in these instances, it is taking the IRS more than 21 days to issue any related refund. If, as a result, a correction is made to any RRC, EITC or ACTC claimed on the return, the IRS will send taxpayers an explanation. Taxpayers are encouraged to continue to check Where’s My Refund? for their personalized refund status and can review Tax Season Refund Frequently Asked Questions.

the IRS has a huge backlog of returns.  even e-filed returns are taking longer to show up in the IRS system than normal.

when you e-file. the IRS sends the transmitter (in your case Turbotax) notification that it was either accepted or not.  Then Turbotax sends you a corresponding e-mail.  since you seem to be saying that you got an acceptance e-mail, the IRS has it.