The two most notable developments in 2020 concerning Google Photos were the end of support for free unlimited storage and the redesign that revolved around Memories. However, the latter only affected the app while the web experience largely remained the same. That's changing, though, as Google is rolling out an update to the web client that offers a similar experience.
First spotted by 9to5Google, the redesign introduces an Explore tab that is the equivalent of the Search tab on the mobile app. Here, you'll be able to sift through your media with the help of three categories: People, Places, and Things, or even sort it on the basis of media type (i.e. screenshots, videos, motion photos, etc.).
While you can access your favorites from within this tab, there's also a dedicated Favorites tab in the navigation menu that will let you directly jump to your starred media. What's still lacking from the web experience, though, is access to Memories which shows a personalized collection of pictures, grouped together either by date or a common theme — scenic sunsets and kitchen escapades, for instance.
At the time of writing, the new update doesn't seem to be widely rolled out. Since I could only spot it on one of my three accounts, you may have to wait a bit for it.