Do I need to keep the Beta Version of PS if I have the 2024 installed? also 2024 does not show up in

It's entirely your choice, but if you are going to keep the beta version, then you need to update it when prompted.  Photoshop beta is the pre-release version, so will have repeated updates.  It is also time limited so will stop working after a while, forcing you to update or stop using the beta version.

If you do decide to keep the beta, you mighht like to follow the Photoshop beta forum, and specifically the two threads pinned to the top of page one, which tell us about ther changes.

no, os beta version is not needed to use ps 2024.

and it's unclear what you mean by 2024 does not show up in the THE MAC APP LIBRARY.  if you install a cc app on a mac, by default, it installs in your applications folder.