"I don't seem to find the option any longer either using the phone app nor the computer browser."
Go to Home & select TuneIn.
Search for the station. It should switch to that and start playing. You'll see the "play bar" at the bottom of the screen, below the list of search results. Tap on the TuneIn or Station icon. (Some stations have their own icon.)
Now the station play bar will fill the bottom of the app.
On the right side, you'll see "Queue" and "History" and the name of the current song underneath.
To the right of the song that's playing will be a little gray down arrow that is hard to see. Tap on that. When you do, you should see the option "Favorite Station" in gray. Tap on that. It should turn red.
Now, go to the Home Screen and tap on TuneIn again. Scroll the right side of the app where it says Browse, Local radio, Trending, etc, to see the bottom of the list.
Under Favorites, you should see your station and you can play them from there.