Should I wait for the IRS letter they claim was sent about my return, or take action now since it's been weeks and I haven't received any notice in mail or online?

Does the IRS site say something like "Take action" or "action required"   or are you just stressing because your refund has not yet arrived?  

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 2024 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/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_US_en_US?uid=lt447ebr

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/turbotax-support/en-us/help-article/tax-refund/refunds-take-longer-others/L14YlqFrH_US_en_US?uid=lexdr7zh

.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/irs-refund-taking-longer-21-days/L2vRAJbdU_US_en_US?uid=lexe7lst

If you are getting earned income credit on line 27 or additional child tax credit on line 28 You are subject to the delay required by the PATH act.  Do not expect your refund before early March

https://turbotax.intuit.com/tax-tips/irs-tax-return/what-is-the-path-act-and-how-may-it-impact-your-taxes/L2fkZJmNC

Note:  “Accepted” is not the same as “approved”.  TurboTax tells you the e-file was accepted if the IRS deems that there is enough information on the return for them to take it in for processing.   Only the IRS can approve of the refund, which is a later stage of processing.  If the IRS approves your refund they will provide a date for the refund to be issued.

Who claims that the IRS sent you a letter? The IRS? How did you find this out?

I think it would be better to give it some more time rather than blindly making a change that may not be at all what the IRS is worried about - if, indeed they are worried about anything at all.

And we don't even know if there was a mistake, much less why someone didn't up on it.