Version information:
This is an original bug that is still present in OpenLoco v25.02.
Describe the bug
If you disable "Play Music" from the ear icon drop-down of the top toolbar while you have the Options - Music window open, the music options will now be out of date, but its visuals will not update until the options window is "invalidated" by something else.
Expected behaviour
When music is disabled, the Options - Music window should immediately change to show the Stop ⏹ button as being selected, and not the Play ▶ button.
Screenshots

(Result of moving another window around the options window after replicating this issue)