After installing Apple OS update to Ventura 13.4.1 on my MacBook, PSE 2021 does not open.
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.
The oldest pse version i have on macOS Ventura is pse 2022, however, you can try the following which may work:
Adobe Photoshop Elements 19 Settings folder
Adobe Photoshop 19 Paths