Did you use the Desktop program? Or the Online web version? Are you using Windows or Mac?
You only need the file ending in .tax2023 to transfer into 2024. Or the .tax2024 to transfer into 2025 next year.
On the old computer, Your tax files end in .tax or .tax2021 or .tax2022 or .tax2023 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 or print your return in the future like to get a mortgage or loan, etc.
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.
The programs need to be installed from the CD or download them again. You don't need to install them unless you need to amend or open a return. They only support the last 3 years so you might not be able to update older years or download any state programs you need.
Since you now have to log into an Intuit Account all your downloads and licenses are listed there (even if you bought it from somewhere else) so if you need to download to install it again or install on another computer, even on the other operating system (Windows, Mac). And the download will always be up to date with all the updates.