No date has been set for the TurboTax update.
Please note that the issuance of a K2/K3 is not a Turbo Tax issue, it is a IRS issue. According to the IRS, these are the release dates for these forms, based on type of Business Entity.
Form 1065 March 20, 2022
Form 1120-S Mid-June 2022
Form 8865 January 2023
For some taxpayers, the IRS has announced that most K2/K3 reporting for 2021 can be delayed until the 2022 tax return. If your K-1 does not report foreign activities for Schedule K-3, you can uncheck the box (14 on 1120S, 16 for 1065) and e-file now.
However, if your K-1 does report foreign activities, you are required to include Schedule K-3. You have the option to uncheck the box, e-file now, and amend your return later. Or you can file an extension and check back later in the year to see if Schedule K-3 is available.
For more info, see this IRS link.