Get rid of most `g_type_class_add_private` occurrences (and use G_DECLARE_..._TYPE)

Sooo, I wanted to do something which wouldn't require too much thinking. Suddenly, I ended up with this MR.

The commits can be squashed, changed in order, ... as they are quite isolated from each other. There are still a few occurrences where g_type_class_add_private is still used, but they should be minimal.