Looks like the web version is lacking it. The apps both desktop and phone support the feature.
One setting is in the apps settings. Auto play will play similar content once the current Playlist ends if repeat (and maybe shuffle?) is off.
In playlists you have made you can toggle Smart Shuffle which mixes recommendations into your shuffled playlist while it is toggled on. It doesn’t seem to work with the radio feature but I think Autoplay does.
Yea, work computers suck, our company blocks spotify at the network so I just have to use my phone and cellular.