Audio notification after a completed task

What sort of tasks are you thinking of? I presume background tasks like exporting, but can you provide some examples?

If you wanted to make a feature request for InDesign, you should post in the InDesign User Voice so it can be seen by product managers and voted on by users:

https://indesign.uservoice.com/

On Mac OS, you can use the applescript "say" command. Through Javascript, that will be something like:

var scpt = 'say "Processing is complete."';
app.doScript(scpt, ScriptLanguage.APPLESCRIPT_LANGUAGE);

On Windows, you would need to use a similar VB command if any.