Where are key words saved?

The keywords are stored in the metadata of the files IF you wrote the metadata to the files in Elements (or took certain other actions which automatically write the metadata to the files).  However, if you did not do that, I believe the keywords are stored in the catalog database file which, for Elements 2019, is named catalog.pse17db (which is found in a folder named the same as your catalog, e.g. My Catalog.  Are you able to retrieve that folder from a computer backup or do you have an Elements backup?  (The default folder location would be C:\ProgramData\Adobe\Elements Organizer\Catalogs so if your system drive was not affected, it should still be there.)

If the catalog folder is available, install Elements 2019 and load the restored catalog.  You can then write the metadata to the files and the keyword tags will be available in other applications.  You would also be able to import the catalog into Lightroom (possibly without writing the metadata to the files). 

If you don't have a backup of the catalog, you can install Elements 2019 and import the files into a new catalog.  During the Import process, you will be given the opportunity to include the exisiting keyword tags into a new tag hierarchy even if the metadata has not been written to the files.  However, there are some other nuances that need attention with respect to system tags (People, Places, Events).  I shall await further information from you before giving your further details.

then carefully adding key words in Elements 2019.

By @brads9934690

I've moved your post from Photoshop to Photoshop Elements for you.

Jane