I upgarded from 2013 to 2020 and the catalog conversion did a terrible job. A lot of my folders are no longer in the catalog and it picked some folders from Explorer.
Did you do a true catalog conversion or did you do a bulk import? When you first opened 2020, you should have received a message asking whether you wanted to convert your Elements 13 catalog. If you said yes, your old catalog would have been converted and it would not have lost anything that existed in your prior catalog. If you clicked one of the buttons that are available in different locations to get your media, then media would only have been gathered from certain locations on your computer. This may be why you think you have lost some folders and gained others you did not want.
In any event, your Elements 13 catalog still exists on your computer and you can convert it either for the first time or again. Go to File>Manage Catalogs and click the Convert button. You should see a list of your catalogs. If you don't see your 2013 catalog, you need to check the Show Previously Converted Catalogs box.
What is the comparison in the number of media files that are displayed in the Media grid? Can you give us a screenshot of your folders panel in each version's catalog.
Thanks for reporting back. I have never heard of a conversion going bad in the way you described.