I have Elements 12 and would like to download a trial of 2021. Will installing the trial of 2021 change the catalog and prevent me from going back to using Elements 12 if the newer Elements doesn't work right? Or should I make a new temporary catalog in 12 and import a few dozen photos into it and then have Elements 2021 open that temporary catalog?
You have no worries- each version installation is it's own separate installation- installing a newer version doesn't nothing to an older version. You will be asked about importing your old catalogue, be like nike and just do it.
Although I am not entirely sure, I believe that during the conversion process, your Elements 12 catalog will be renamed with a -1 suffix and the Elements 2021 catalog will be given the name of your old catalog. So, when you try to open the Elements 12 Organizer, you will get a message that the catalog cannot be found (because it has been renamed). If you save your catalogs in the default location, you should be able to open a Manage Catalogs>browse dialog and find the renamed catalog.