You can buy 2022 Desktop program here,
Have you moved your prior year files to the new computer?
What I would do is just copy the whole Turbo Tax folder that is under your Documents. That should be where the .tax files and pdf files are stored. Copy that folder to a flash drive or best yet is to burn it to a CD or DVD and then you will have a backup of them. Then on the new computer copy the folder (or files) from the flash drive to your Documents folder.
You only need the tax return data file ending in .tax2021 to transfer into 2022. You don't need to install older programs unless you need to amend or you didn't save the pdf file.
See this article on how to move your tax return to another computer…….
It's not clear whether you are trying to use TurboTax Online or the CD/Download TurboTax software ("desktop"). It sounds like you might have used the CD/Download software for 2021, and are trying to use TurboTax Online for 2022.
There is no connection between TurboTax Online and the CD/Download software. TurboTax Online doesn't know what you filed with the CD/Download software, and the CD/Download software doesn't know what you filed with TurboTax Online.
TurboTax Online for 2022 is not available yet. It should be available in early to mid December. That's why, if you sign in to TurboTax Online now, it still refers to 2021.