Summary:
As a preparation for further changes clean up the Compositor
class. First step is to use the new slot syntax and rename
some of the slots.

Includes some other minor code style improvements to the class
as well.

Test Plan: Manually in X and Wayland nested session.

Reviewers: #kwin, zzag

Reviewed By: #kwin, zzag

Subscribers: davidedmundson, zzag, kwin

Tags: #kwin

Maniphest Tasks: T11071

Differential Revision: https://phabricator.kde.org/D22218