fix(bots): auto-join server from channel_id so built-ins can post

Root cause: makeSender requires bot_servers membership, but create
flow never auto-added bots when users only picked a channel.

- Start() resolves config.channel_id → server and upserts bot_servers
- Confess cursor uses (created_at,id) so deletes don't stall polling

internal/bot/runner.go

@@ -82,6 +82,10 @@ func (r *Runner) Start(botID, botType string, config json.RawMessage) {
 	r.bots[botID] = cancel
 	r.mu.Unlock()
 
+	// Built-in bots pick a channel in config but users often skip "Add to Server".
+	// Resolve channel_id → server and ensure bot_servers so send() doesn't no-op.
+	r.ensureBotServerFromConfig(botID, config)
+
 	send := r.makeSender(botID)
 	r.logger.Info("starting built-in bot", "bot_id", botID, "type", botType)
 
@@ -96,6 +100,36 @@ func (r *Runner) Start(botID, botType string, config json.RawMessage) {
 	}()
 }
 
+// ensureBotServerFromConfig joins the bot to the server that owns config.channel_id.
+func (r *Runner) ensureBotServerFromConfig(botID string, config json.RawMessage) {
+	var cfg struct {
+		ChannelID string `json:"channel_id"`
+	}
+	if err := json.Unmarshal(config, &cfg); err != nil || cfg.ChannelID == "" {
+		return
+	}
+	serverID, err := r.hub.ServerIDForChannel(context.Background(), cfg.ChannelID)
+	if err != nil || serverID == "" {
+		r.logger.Warn("bot start: channel not found for auto-join", "bot_id", botID, "channel_id", cfg.ChannelID, "error", err)
+		return
+	}
+	var ownerID string
+	if err := r.db.QueryRowContext(context.Background(),
+		`SELECT owner_id FROM bots WHERE id = $1`, botID,
+	).Scan(&ownerID); err != nil {
+		return
+	}
+	if _, err := r.db.ExecContext(context.Background(), `
+		INSERT INTO bot_servers (bot_id, server_id, added_by)
+		VALUES ($1, $2, $3)
+		ON CONFLICT DO NOTHING
+	`, botID, serverID, ownerID); err != nil {
+		r.logger.Warn("bot start: auto-join server failed", "bot_id", botID, "server_id", serverID, "error", err)
+		return
+	}
+	r.logger.Info("bot auto-joined server", "bot_id", botID, "server_id", serverID)
+}
+
 // Stop stops a single bot by ID.
 func (r *Runner) Stop(botID string) {
 	r.mu.Lock()