docs: Build API documentation using gi-docgen

This is not a library so it is not really useful for external consumers but it is still nice to have as a development reference.

I plan to add more documentation while wrapping my head around individual components

Had to move the --instrospect-dump flag capture outside the GApplication since that initialized bunch of classes that bind GSettings in their constructors and thus need access to schemas, which are not yet available when building in a sandbox. The option parser itself adds GTK options, which triggered GTK to check for display server.