No, you don't have to move all of the old program files unless you need to amend those old returns.
To get your 2023 return done, you will need just 2023 and 2022. Moving 2022 over is just to make sure your tax information rolls over with no issues.
The only reason to reinstall the older programs would be to amend them. That being said, do keep a PDF of the last three returns on your new computer.