In previous versions (currently using 3.12.4) the square stop button actually stopped the music and cleared the progress bar. This ensured the soundcard was released.
Current version (3.16.1) the stop button pauses the music and doesn’t clear the progress bar and from what I can see the soundcard is not released.
The stop facility is useful when using Snapcast in a multi room scenario, as it would free the soundcard on an individual machine, without having to restart mopidy, this would then let snapcast broadcast through it.