refactor: extract standalone chat package from game-specific handlers

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.

features/snakegame/pages/game.templ

@@ -3,6 +3,8 @@ package pages
 import (
 	"fmt"
 
+	"github.com/ryanhamamura/c4/chat"
+	chatcomponents "github.com/ryanhamamura/c4/chat/components"
 	"github.com/ryanhamamura/c4/features/common/components"
 	"github.com/ryanhamamura/c4/features/common/layouts"
 	snakecomponents "github.com/ryanhamamura/c4/features/snakegame/components"
@@ -26,7 +28,7 @@ func keydownScript(gameID string) string {
 	)
 }
 
-templ GamePage(sg *snake.SnakeGame, mySlot int, messages []snakecomponents.ChatMessage, gameID string) {
+templ GamePage(sg *snake.SnakeGame, mySlot int, messages []chat.Message, chatCfg chatcomponents.Config, gameID string) {
 	@layouts.Base("Snake") {
 		<main
 			class="snake-wrapper flex flex-col items-center gap-4 p-4"
@@ -43,13 +45,13 @@ templ GamePage(sg *snake.SnakeGame, mySlot int, messages []snakecomponents.ChatM
 				if sg.Mode == snake.ModeMultiplayer {
 					<div class="snake-game-area">
 						@snakecomponents.Board(sg)
-						@snakecomponents.Chat(messages, gameID)
+						@chatcomponents.Chat(messages, chatCfg)
 					</div>
 				} else {
 					@snakecomponents.Board(sg)
 				}
 			} else if sg.Mode == snake.ModeMultiplayer {
-				@snakecomponents.Chat(messages, gameID)
+				@chatcomponents.Chat(messages, chatCfg)
 			}
 			if sg.Mode == snake.ModeMultiplayer && (sg.Status == snake.StatusWaitingForPlayers || sg.Status == snake.StatusCountdown) {
 				@snakecomponents.InviteLink(gameID)