How can I get a copy of my 2021 taxes from TurbTax if I did not download it that year?

  You have to access your own account and/or  print it for yourself using exactly the same account and user ID that you used when you prepared the return.

Start a 2022 return online and enter some personal information  so that the menu on the left opens up and lets you access your past year returns.

https://ttlc.intuit.com/community/prior-year-return/help/how-do-i-access-my-prior-year-return/01/27010

Many people have multiple TT accounts and forget how to access them.  Log out of the account you are in now.

Account Recovery

https://ttlc.intuit.com/questions/1901535-forgot-your-turbotax-online-user-id-or-password

Or did you use the desktop version of TurboTax?  If so, the files are on your own hard drive or any backup device you used like a flash drive.

https://ttlc.intuit.com/questions/1901486-how-many-turbotax-accounts-do-i-have

https://ttlc.intuit.com/questions/1901535

https://ttlc.intuit.com/questions/1901659-find-your-tax-data-file-in-mac

https://ttlc.intuit.com/questions/1900721-find-your-tax-data-file-tax-file-in-windows

To get a copy of your previously filed returns prepared with online TurboTax https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-in-turbotax-online