feat(ui): BOTS section in member list

Members API appends server bots (is_bot). Sidebar groups ONLINE / OFFLINE / BOTS.
Bots get green BOT badge, no kick menu or profile. Mentions and DMs skip bots.

internal/server/members.go

@@ -35,6 +35,8 @@ type memberResponse struct {
 	Avatar      string  `json:"avatar"`
 	Status      string  `json:"status"`
 	StatusText  string  `json:"status_text"`
+	IsBot       bool    `json:"is_bot,omitempty"`
+	BotType     string  `json:"bot_type,omitempty"`
 }
 
 func (h *MemberHandler) ListMembers(w http.ResponseWriter, r *http.Request) {
@@ -82,6 +84,28 @@ func (h *MemberHandler) ListMembers(w http.ResponseWriter, r *http.Request) {
 		members = append(members, m)
 	}
 
+	// Bots added to this server (separate BOTS section in the member list).
+	botRows, err := h.db.QueryContext(r.Context(), `
+		SELECT b.id, b.name, COALESCE(b.avatar, ''), COALESCE(b.bot_type, '')
+		FROM bot_servers bs
+		JOIN bots b ON b.id = bs.bot_id
+		WHERE bs.server_id = $1
+		ORDER BY b.name
+	`, serverID)
+	if err == nil {
+		defer botRows.Close()
+		for botRows.Next() {
+			var m memberResponse
+			if err := botRows.Scan(&m.ID, &m.Username, &m.Avatar, &m.BotType); err != nil {
+				continue
+			}
+			m.DisplayName = m.Username
+			m.Status = "online" // ponytail: no bot presence yet; always show online
+			m.IsBot = true
+			members = append(members, m)
+		}
+	}
+
 	w.Header().Set("Content-Type", "application/json")
 	json.NewEncoder(w).Encode(members)
 }