You can use a Google Sheets add-on "Photo Gallery" to create a slideshow with Google Slides, from photos in your Drive. You can then insert this slideshow in a site (either classic or new).
- In Google Drive create a new spreadsheet.
- Install this Add-on https://chrome.google.com/webstore/detail/photo-gallery-by-awesome/jgkjnffgfnibcjeedannoakcdnjlncmm
- Click Add-ons and select Photo Gallery by Awesome table.
- In the right hand column select a folder in your drive that contains the photos you want in your gallery.
- Continue to create the slideshow.
- When finished click to view the Slideshow that has been created.
- In your web site in the insert menu click Slides under Google Embeds and select the newly created Slideshow. (Remember to change its sharing to public).
CREDIT: Add-on created by Romain Vialard and there are more instructions on his web site.
"As Picasa / Google Photos has deprecated its slideshow feature, one remaining solution was to add your photos as slides of a Google presentation. But this can be very time consuming if you have many photos!
Thanks to our add-on, you can simply put all your photos in a Drive folder and we will automatically insert them in a Google Slides presentation that you can embed in any website."
See an example below. Note: on a mobile device the slideshow doesn't start until the viewer clicks on it to open it.