Rewrite Savegame page to use class syntax, enabled by rP22923 / D2290, refs #5387.

Uses simple event subscription to make the classes independent of each other.
Removes all globals except two variables and one function (that may be avoided in the future too).
Allows the reader to focus on the relevant aspect of the implementation (encapsulation, information hiding) and makes implementation more modifiable and extensible.

Differential Revision: https://code.wildfiregames.com/D2310