The new google sites at this time has several ways to embed your Google Photos into the site. Many of them require using awesome tables. Here are a list of five different options that I have found to be useful for adding images to New Google Sites. Of course, Google keeps adding features to Sites, so this could change any day.
Awesome Table Photo Gallery from an Album
This is an example of a Google Photos album embedded in the site with the Photo Gallery by Awesome Table add-on. As you can see from the example, each photo will open in a new tab for a full screen view of the photo.
A second way to at least put a link to a Photo Album is to simply get the link from your Google Photo album and paste it here. What you will then get is one picture as you see which is a link to the album. These two work great in combo.
Photo Gallery Slides
This is also from the awesome table photo gallery add-on, it is the google slide stack that the add on automatically creates from the google photo album. If you update the album, you can rerun the add-on and the slideshow and the photo gallery update.
Awesome Table Slideshow View
Another option is to also use awesome table and create the new awesome table slideshow view of your spreadsheet. This is the same spreadsheet that the Photo Gallery is based on. I then duplicated the sheet that the add-on created so I could add the correct Awesome table filters to make this view work.
Of course a final way is to statically add each image to the page and attach some text to the bottom of each