Moving the updater to the new logging system

This is a fairly major refactor of the updater's logging and error handling. I haven't tested it throughly yet, we'll need to do that when we're testing updates as usual before the release.

Related to https://github.com/KanoComputing/peldins/issues/859 and https://github.com/KanoComputing/peldins/issues/873

cc @alex5imon