Does TurboTax automatically save the government and TurboTax worksheets as well as the tax return?

Yes, all of the worksheets are available for the 2024 tax return if you use Print Center and the option for all worksheets.

Click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.  Choose the option Include government and TurboTax worksheets

The program saves everything for only 7 years, which is why you need to download everything for your records.