It takes the IRS longer to process a return that was filed by mail. Wait about four weeks and start checking on the IRS refund site to see if it is being shown yet. And....for the future---when you mail a tax return use a mailing service like certified mail so you can track it and know for sure that the IRS received it.
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:
https://www.irs.gov/refunds
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund