When you install Elements 2021 and launch the Organizer, you will be asked whether you want to use your old catalog. (I don't remember the exact wording, and it is easy to miss - so pay attention when first launching the program.) If you respond yes/OK, the new program will copy your old catalog and rename it with a suffix -1. It will then convert your old Elements 13 catalog to the new format and everything will appear the same.
The Organizer is simply a catalog of the photos/videos stored on your computer. So nothing else needs to be copied. They will be transferred automatically.