Add <timer-player-button> with tests.

[Works towards #45461541, closes "Add tests for <timer-player-button>"]
Rename <timer-play-button> to <timer-start-button>

[Works towards #45461541]
<timer-start-button> tests are green.

Also MainCtrl now simulates timer/update events only after receiving
a timer/start event from the <timer-start-button> being clicked.

[Finishes #45461541]