The TurboTax software will be updated to the 2021 contribution limits after the IRS finalizes the forms, schedules and instructions for the HSA contribution limit.
The IRS has most all 2021 forms, schedules and instruction in draft mode and will not finalize until January and February of 2022. Go to this IRS draft form website - https://apps.irs.gov/app/picklist/list/draftTaxForms.html
The availability dates of IRS forms will be shown using this TurboTax support FAQ sometime in mid-December - https://ttlc.intuit.com/community/forms/help/irs-forms-availability-table-for-turbotax-individual-personal-tax-products/00/26224
BUT... the HSA limits have been set for years... Heck, I already know 2022 is $8300. You don't need to wait for the IRS. 2021 is $8200. Done.
I concur with gdevitry2. Although the forms may not be final, the numbers are known and it should be trivial for Intuit to update the 2020 form they're temporarily using with the 2021 numbers they know are correct for 2021, even as they wait for any other changes to the forms. TT loses its value as a tax planning tool between release and end of year when numbers are not updated to what is already known.