autosave: Adapt to changes in picard.File.save

In Picard commit e40e1f393be96cc63445a89a84ea9e89a3fa7279, file.save
was converted to use thread pool tasks instead of next_action chaining.
Unfortunately, this removed a clean way to run code after all the
tasks are done.

It looks like monkeypatching an _internal method is now the cleanest way
to achieve what this plugin needs to do, so use that.
autosave: Refactor & comment the code a bit