The organization data is stored in a catalog folder. The default location is C:\ProgramData\Adobe\Elements Organizer
If you still have Elements 19 installed on your old catalog, you can go to the Organizer's Help>System Info . . and it will tell you the name and location of the catalog folder (if you have moved and/or renamed it). You can copy this folder to your new computer or move it to your external drive - it doesn't matter where it is located.
You should install Elements 2025 on the new computer. Then, assuming that your external drive has the same drive letter on your new and old computer, you should go to the Catalog Folder in Windows File Explorer and double-click on the file named Catalog.pse17db. This should launch Elements 2025 and you will be asked whether you want to convert your catalog to Elements 2025. The conversion process takes a while, but once it is completed, all of your photos should be present in the catalog on the new computer.
If double-clicking on the catalog file doesn't work as I expect, go to File>Manage Catalogs and click on the Convert button. In the dialog that opens, navigate to the catalog folder. Select the catalog in a list that appears and click the second Convert button.