TurboTax never gets any information from the IRS after you file a tax return so not sure why anyone would have suggested to you that TT would know. Maybe you talked to someone who doesn't know much.
Did you e-file the 1040X or did you mail it? If you e-filed---was it accepted? If you mailed it did you use tracking so you know it was received?
Even during “normal” times it takes about four months for the IRS to process an amended return. During the pandemic and due to the severe backlog at the IRS it is taking much longer—six months or more for many amended returns. Do not expect quick results from amending. When the IRS issues a refund for an amended return it will be by check. They do not make direct deposits for refunds for amended returns. You can watch for information here:
https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1
Per the IRS:
Status of Processing Form 1040-X, Amended Individual Tax Return: As of January 1, 2022, we had 2.3 million unprocessed Forms 1040-X. We are processing these returns in the order received and working hard to get through the inventory. The current timeframe can be more than 20 weeks instead of up to 16. Please don't file a second tax return or contact the IRS about the status of your amended return. Taxpayers should continue to check Where's My Amended Return? for the most up to date processing status available.
IRS Operations During COVID-19: Mission-critical functions continue | Internal Revenue Service