Here is a summary of the ways you can start or resume execution in debug mode.
Choose Script > Execute or Script > Resume (they are the same menu item).
Or, click Execute or Resume in the toolbar (they are the same button).
Choose Script > Trace.
Or, click Trace in the toolbar.
Issue any Step command.
You cannot issue Step Out as a way of starting execution of a script, because when the script is stopped you’re not “in” anything.
Issue the Execute (or Trace) to Here command. This effectively sets a breakpoint and starts or resumes execution at the same time.
The ability to test individual handlers (and the event history) applies in debug mode exactly as in normal mode, only even more so! Not only Execute but also Trace and the Step commands have the Event Handler menu. (But not Step Out, because it can’t be used to initiate execution from a stopped state.)