feat(bots): bot framework polish + store

- /ws/bot endpoint: bot token auth via query param, SHA-256 lookup
- Bot WS actions: SEND_MESSAGE + DELETE_MESSAGE handled in gateway
- Bot messages: bot_id on messages table, bot badge in chat (green + BOT tag)
- Bot store: /bots lists all bots with server count + add-to-server
- Bot manager moved to /bots/manage
- Fix: command routes were double-nested under /bots/{botID}/commands
- Fix: fetchServerCommands route corrected to /bots/servers/...

internal/bot/handlers.go

@@ -22,6 +22,7 @@ func NewHandler(db *sql.DB) *Handler {
 
 // RegisterRoutes registers authenticated bot routes under the given router.
 func (h *Handler) RegisterRoutes(r chi.Router) {
+	r.Get("/store", h.Store)
 	r.Post("/", h.Create)
 	r.Get("/", h.List)
 	r.Get("/{botID}", h.Get)
@@ -547,3 +548,54 @@ func (h *Handler) RegenerateToken(w http.ResponseWriter, r *http.Request) {
 
 	writeJSON(w, http.StatusOK, b)
 }
+
+// ---- Store (public listing) ----
+
+type storeBotResponse struct {
+	ID          string  `json:"id"`
+	Name        string  `json:"name"`
+	Avatar      *string `json:"avatar"`
+	Description string  `json:"description"`
+	ServerCount int     `json:"server_count"`
+	OwnerID     string  `json:"owner_id"`
+	CreatedAt   string  `json:"created_at"`
+}
+
+// Store returns all bots with their server count (visible to any authenticated user).
+func (h *Handler) Store(w http.ResponseWriter, r *http.Request) {
+	rows, err := h.db.QueryContext(r.Context(), `
+		SELECT b.id, b.name, b.avatar, b.description, b.owner_id, b.created_at::text,
+			   COUNT(bs.server_id) AS server_count
+		FROM bots b
+		LEFT JOIN bot_servers bs ON bs.bot_id = b.id
+		GROUP BY b.id, b.name, b.avatar, b.description, b.owner_id, b.created_at
+		ORDER BY server_count DESC, b.name
+	`)
+	if err != nil {
+		writeErr(w, http.StatusInternalServerError, "server error")
+		return
+	}
+	defer rows.Close()
+
+	bots := make([]storeBotResponse, 0)
+	for rows.Next() {
+		var b storeBotResponse
+		var avatar sql.NullString
+		var createdAt sql.NullString
+		if err := rows.Scan(&b.ID, &b.Name, &avatar, &b.Description, &b.OwnerID, &createdAt, &b.ServerCount); err != nil {
+			writeErr(w, http.StatusInternalServerError, "server error")
+			return
+		}
+		if avatar.Valid {
+			b.Avatar = &avatar.String
+		}
+		b.CreatedAt = createdAt.String
+		bots = append(bots, b)
+	}
+	if err := rows.Err(); err != nil {
+		writeErr(w, http.StatusInternalServerError, "server error")
+		return
+	}
+
+	writeJSON(w, http.StatusOK, bots)
+}