Where did you read that ? Also see this thread: Monterey upgrade ok?
The current version of Audacity is 3.1.3. Note that it uses a new project format .aup3, so everything is contained within one file. Prior to 3.0.0, an .aup file contained pointers to thousands of tiny .au files which held the actual audio. Audacity 3.1.3 will import the old .aup-based projects and save them in the new .aup3 format.
So I’m thinking the new computer will not have the old version of Audacity loaded on it to begin with. So just download and install a fresh copy from Audacity ® | Downloads.
But if you are just updating the old computer, then yes, it is generally a good idea to uninstall the old version before installing the new. You can download older version of Audacity from: Old Audacity versions download