Updates are not available for any of the years from 2018 to the current tax year, so installing those CD's will not help you much beyond making it easier to print the returns from the earlier years. IF you also transfer the tax files to the new computer from a flashdrive, etc.
updates are unavailable for 2018 and prior. those CD's are beta versions that can't be updated. and if you filed state returns for any of those years the state program is not available. if you open those returns using the reinstalled apps, there is a possibility that you'll end up with a return that is different from what was filed and you will not be able to access the state return.
if you want copies of those returns there is a website that offers to print those returns by e-mailing them the xx tax20xx file
we don't vouch for this website but others have used it and there have been no negatives posted on this forum about them. there is a fee for each return.
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And....as for installing the CD's----many new computers do not have disc drives, and the downloads are not available for the years earlier than 2018. Not sure what you meant when you mentioned installing on "cloud."
For Windows. Your tax files end in .tax or starting in 2008, .tax2008, .tax2018, .tax2019, .tax2020 etc. They should be in your Documents in a Turbo Tax folder. You should also have the pdf files of each year. Or search your computer for all files ending in .tax. Also if you haven't done it, I would open each year in the program and save it as a pdf file, go to FILE - SAVE TO PDF so you don't need the program installed to view your return.
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 .tax2020 to transfer into 2021. 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…….
https://ttlc.intuit.com/community/tax-data-file/help/how-do-i-move-my-tax-data-file-to-another-computer/00/26128
After you get the program reinstalled the first thing to do before you open your tax return is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW). Enter some basic information, then go to the state tab and download the state program. Then try to open your existing return, go to FILE - OPEN
Going forward ALWAYS save a PDF of the return (with and without the worksheets) AND the .taxfile for every return you file. Also save them to a removable storeage medium or 2 for safe keeping. This way you always have access to the returns even if you no longer have access to the programming or the original computer you did them on.