Picasa Web Albums is no more but your photos are still available on Google Photos.
To insert a photo into a Google Site use Insert>>Google+>>Photo
Using Insert>>Image>>Web address and inserting the sharing URL from Google Photos does not work!
One problem exists: When inserting a new photo in Google Photos and you make it "Shared" it will appear in your site but when a viewer clicks it to view the full-sized image it will not appear unless the viewer is signed in with a Google account. Public photos transferred over from Picasa Web albums work OK.
A work-around is to post the image in a Google+ public post. Doing so apparently makes the image fully shared.
Google is aware of the problem but apparently are unable to do a quick fix.