PSE 2021 cannot run on Apple OS Ventura 13.4.1

The oldest pse version i have on macOS Ventura is pse 2022, however, you can try the following which may work:

Go to

Macintosh HD/Users/UserName/Library/Preferences

and trash

Adobe Photoshop Elements 19 Settings folder

Adobe Photoshop 19 Paths

com.adobe.PhotoshopElements.plist

Elements 2021 is not compatible with the Ventura OS.  See this Adobe HelpX article.  However, see this discussion where @Jeff Arola, another Community  Expert says that Elements 2022 works on his Mac machine even though it is not listed as compatible in the article.  Jeff may be able to let us know whether he has had any luck with Elements 2021 and Ventura.