The Google Photos progressive web app is available for Chrome on Android and desktop versions, so you should be able to see it pop up for you as an option moving forward now that Google has enabled the capability. That being said it may still require some users to enable the flag for PWAs, so if you tap on the overflow menu and don't see the option to install the Photos PWA, then enabling the flag is the likely solution. While Photos can already be installed on your device through the Google Photos Android app, and through Chrome on desktop as a Chrome app, the progressive web app version should be quicker to use.
Head over to the Google Photos website – photos.google.com, and tap on the overflow menu in the browser (the three little dots in the right-hand corner of the browser user interface) and the option should be listed more towards the bottom, below the zoom option and just above the edit, cut, copy, and paste options. If you're looking at the site in Chrome for Android, it may be listed higher or lowers in the overflow menu as Chrome for Android does not have the exact same set of options here, so that's worth keeping in mind.
If you don't see the option and you need to enable the Chrome flag, simply tap or click the address bar and the type chrome://flags/#enable-desktop-pwas and that will bring up the flag you need to flip the switch on in order to install progressive web apps on your desktop or Android smartphone or tablet. From there, it's as simple as going back to the Google Photos website, tapping the overflow menu again, finding the "install Google Photos" PWA option and following through. If you're installing the PWA on your Android device the icon for it will show up on your homescreen, and if you're installing on your computer then it'll show up on your desktop.