Sorry, it's not possible to use the Organizer after the trial period without licensing. I think that was possible with much older versions.
A new version (PSE2020) is awaited in the coming weeks. Instead of buying PSE2019, I suggest downloading the new version as a trial when it's available. You'll be entitled to convert your PSE2019 catalog to the new version and use it for 30 days after which you'll have to license it.
Note that users of Lightroom classic can convert PSE catalogs to the LR format and recover practically all your organization.
If you don't want to continue with Elements Organizer, my advice is still to use the next trial version and to convert your catalog. Then you can 'write metadata to files' to make your tags and captions available to any other external managing software, including Explorer/Finder (and why not, in Bridge, which is free even if you don't subscribe to a Photographer's plan). Or you can re-import your files with tags and captions into an older licensed version of the Organizer.