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.

chat/persist.go

@@ -0,0 +1,45 @@
+package chat
+
+import (
+	"context"
+	"slices"
+
+	"github.com/ryanhamamura/c4/db/repository"
+
+	"github.com/rs/zerolog/log"
+)
+
+// SaveMessage persists a chat message to the database.
+func SaveMessage(queries *repository.Queries, roomID string, msg Message) {
+	err := queries.CreateChatMessage(context.Background(), repository.CreateChatMessageParams{
+		GameID:    roomID,
+		Nickname:  msg.Nickname,
+		Color:     int64(msg.Slot),
+		Message:   msg.Message,
+		CreatedAt: msg.Time,
+	})
+	if err != nil {
+		log.Error().Err(err).Str("room_id", roomID).Msg("failed to save chat message")
+	}
+}
+
+// LoadMessages loads persisted chat messages for a room, returning them
+// in chronological order (oldest first).
+func LoadMessages(queries *repository.Queries, roomID string) []Message {
+	rows, err := queries.GetChatMessages(context.Background(), roomID)
+	if err != nil {
+		return nil
+	}
+	msgs := make([]Message, len(rows))
+	for i, r := range rows {
+		msgs[i] = Message{
+			Nickname: r.Nickname,
+			Slot:     int(r.Color),
+			Message:  r.Message,
+			Time:     r.CreatedAt,
+		}
+	}
+	// DB returns newest-first; reverse for chronological display
+	slices.Reverse(msgs)
+	return msgs
+}