No, it is not required to file the prior year returns before the 2022 return.
Unless you have certain carryover amounts that need to entered from 2020 to 2021 to 2022, then you need to complete those returns before completing and filing a 2022 return. Such as capital loss carryovers, carryovers for Home Energy Credits, carryovers of charitable contributions and the like.
To complete and file a 2020 and 2021 tax return using TurboTax you would need to purchase, download and install on a personal computer one of the desktop editions for each tax year from this website - https://turbotax.intuit.com/personal-taxes/past-years-products/
A 2020 and 2021 tax return can only be printed and mailed, they cannot be e-filed. Use separate envelopes for each tax year when mailing.
