Fix to use server-sent state for whether player has answered/judged

Previously we were using a component state Boolean "submitted" for
this information, but that's fundamentally broken since if the client
reloads the page that state is lost, resulting in the user being
presented with the form as to submit a second time (which is not
allowed by the game).

So, now the rendering looks to see whether the current player's name
is in the list of submitted players, and if so, it does not display
the form. This is exactly what we want.