When you think about it, there had been a simple 'engine' available for centuries - the windlass or capstan. So the donkey engine and winch, being non-portable, would do the jobs that the capstan or windlass had done, such as anchor work, warping and heavy lifting. It was in the same period that extra yards were added to make sail work easier (upper and lower topsails and topgallants) and keep the crew size down.

I suppose one problem with a steam donkey boiler would be the time taken to get steam up, or the waste of fuel in keeping boiler pressure, so I imagine the work done would be the sort that could be predicted.

I've no real knowledge of this, I should say, I'm just thinking aloud (as it were). But I'll look up some of my source books if I get the chance.