As of this writing, v5.6.3 is not "officially" released, but it is available to download for everyone. If you have POP Peeper Pro and have the early release updates enabled, go to Help / About and press "Check version" to update. Otherwise, use the download link below.
May 6 update: v5.6.3 is now live.
Gmail's imposed deadline (Apr 23) has passed and Oauth2 continues to work. v5.6.3 brings back Oauth2 just as before. If Oauth2 fails, POP Peeper will provide the help link so you can review your options.
https://www.esumsoft.com/download/