Port the saving code away from NetAccess

Test Plan:
Saving works. Saving as another existing file brings up the
overwrite prompt. Confusingly, "Save as" and chosing the current filename
doesn't, unlike in other apps, but it's on purpose (and actually makes sense).

Reviewers: broulik, andreagenor, tcanabrava

Reviewed By: broulik

Maniphest Tasks: T11576

Differential Revision: https://phabricator.kde.org/D25479