[server] Use cached current mode more and assert validness

Summary:
We can use the cached current mode in one more case. Additionally make it
more explicit what a valid mode is and when to add them.

Test Plan: Relevant autotests pass. KWin Wayland nested and DRM session work.

Reviewers: #kwin, davidedmundson

Reviewed By: #kwin, davidedmundson

Subscribers: kde-frameworks-devel

Tags: #frameworks

Differential Revision: https://phabricator.kde.org/D23535