‘Listen Now’ was introduced in the iOS 14, iPad OS 14, and macOS Big Sur betas so has now made its way to the browser version of Apple Music.
The new tab is a slightly updated way for the appt o try and surface improved music suggestions to Apple Music subscribers. Like any algorithmic suggestion feature, it should improve the more you use it.
The website also has an updated design that reflects the changes made in the latest versions of the Music app for iOS and macOS. The left taskbar icons are now all red, and the app is filled with new-look artwork.
Like most web versions of music apps, Apple Music’s beta site is pretty limited, and it is likely designed to annoy you enough with its limitations for you to use the app. You can still access the older version of the website (not in beta) here.