They can't force you to buy 2021 product first to get access to prior online returns, because Online TurboTax doesn't even charge one for their 2021 return until the end. Online TurboTax is always "Start for free."
Don't try to get the return from that privacy page (your second screen image), which mainly offers one the opportunity to request all the data that Intuit has file on someone. That screen looks outdated anyway, since it references "an immediate copy of the 2018 return." . Don't try to get the past return that way.
That first screen you provided also has a typo in it. Looks like it was not updated from last year. It says "To download your prior-year returns, just get started with your "2020" (sic) tax return in the product that is right for you." It should say 2021.
It clearly says "just get started." And your image has a blue button "Select a product on Tax Home." What happens when you choose that blue button? Can you proceed far enough that you eventually get Tax Home and Documents as tabs in the left menu column?
