Migrate all users to using the InputModel.

These will be going away shortly.

This adds an 'initial state producer' to create the burst of
state clients will receive on connect, and serialisers for
WindowModels and BackBuffers.

The handler can't be dependency injected (as it's created by the
framework) so, in order to minimise the amount of static
horribleness, pass in a controller which can do the actual work
and have proper dependencies.

Now with working dependencies and webserver.