TurboTax does not receive any information from the IRS after you file your tax return; TT has no knowledge of nor any involvement with your identity verification with the IRS.
Sometimes the IRS chooses returns randomly to request verification of identity and sometimes there is something on the return that triggers the request.
It can take nine weeks or more to receive your refund after verifying your identity with the IRS. You can watch the IRS refund site for information. TT will not have any information.
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/identity-theft-fraud-scams/identity-verification-for-irs-letter-recipients
It sounds like you already got the answer to your question. Whoever "they" are that you called (the IRS?) told you it takes 9 weeks, and xmasbaby0 said the same thing. You said you verified on May 12, which is only 4 weeks ago. So it looks like you should expect to wait another 5 weeks. And I would take that to be an estimate, not a guarantee.