Move SaveMessage/LoadMessages logic into Room as private methods.
NewPersistentRoom auto-loads history and auto-saves on Send, removing
the need for handlers to coordinate persistence separately.
Create chat/ package with Message type, Room (NATS pub/sub + buffer),
DB persistence helpers, and a unified templ component parameterized by
Config (CSS prefix, post URL, color function, key propagation).
Both c4game and snakegame now use chat.Room for message management and
chatcomponents.Chat for rendering, eliminating the duplicated
ChatMessage types, chat templ components, chatAutoScroll scripts,
color functions, and inline buffer management.
