That tax law has not yet been signed into law by the President. When that happens then the IRS will need to change the tax forms, the programmers have to change the software, and then the IRS has to approve of their software. That will take time---we do not know yet when all of those changes will be accomplished. As soon as more is known, TurboTax will provide information.
We don't have specific information on the income qualifications or procedures for the tax changes including a third stimulus payment because the measure hasn't been passed yet.
The Senate bill includes a provision to make the first $10,200 in unemployment insurance in 2020 non-taxable. See this news article.
If that is put into law, that will be a monumental task with so many people already having filed their 2020 tax return and forcing them to file an amended 2020 tax return.
If the law were passed today, it would be hard to imagine the IRS could issue regulations and software providers could provide software changes by April 15.
You can find the most up to date information from the IRS here, and updates from TurboTax here as they develop.