uninstall a programme

The application is not doing anything because it is too old to run in your OS, and sonid the uninstaller that came with it.

As I wrote before you can just drag it to the trash. Any remnants will probably be insignificant. You can run Etrecheck to see if there are any daemons or agents left - even though those are probably not running either, for the same reasons.

Source of below https://helpx.adobe.com/photoshop-elements/kb/uninstall-premiere-elements-photoshop-elements.html

Uninstall from macOS

1. Open Finder and navigate to /Applications/Utilities/Adobe Installers.
2. Start the Uninstaller for Adobe Photoshop Elements or Adobe Premiere Elements.
3. (Optional) If you don't want to keep the application preferences, select Remove Preferences. 
4. Click Uninstall and follow the onscreen instructions to remove the application.
5. Note:
6. If you get any error message or the application is still visible, try reinstalling the application and then uninstall. 

It is Rare I suggest an Uninstaller but this one has come to me attention of another Contributor.

Have never used it personally but the source of the suggested Application is A respected Contributor of long standing.

AppDelete Paid or Trial version

Just drag the application to the trash.

And as a side note: every time you migrate to a new mac or upgrade to a new OS, it is best to start fresh and only migrate the user accounts. This way old stuff will never come along and you avoid not just the present situation (which is innocuous, since the old stuff just doesn’t work) but wose, when old stuff runs amok in the new system.

Is Photoshop Elements 12 the only Adobe app you have installed and use?