[mqtt] Eliminate per-entity loop overhead and heap churn (#13356)

esphome/components/mqtt/mqtt_client.cpp

@@ -403,6 +403,12 @@ void MQTTClientComponent::loop() {
 
         this->last_connected_ = now;
         this->resubscribe_subscriptions_();
+
+        // Process pending resends for all MQTT components centrally
+        // This is more efficient than each component polling in its own loop
+        for (MQTTComponent *component : this->children_) {
+          component->process_resend();
+        }
       }
       break;
   }

esphome/components/mqtt/mqtt_component.cpp

@@ -308,16 +308,12 @@ void MQTTComponent::call_setup() {
   }
 }
 
-void MQTTComponent::call_loop() {
+void MQTTComponent::process_resend() {
-  if (this->is_internal())
+  // Called by MQTTClientComponent when connected to process pending resends
+  // Note: is_internal() check not needed - internal components are never registered
+  if (!this->resend_state_)
     return;
 
-  this->loop();
-
-  if (!this->resend_state_ || !this->is_connected_()) {
-    return;
-  }
-
   this->resend_state_ = false;
   if (this->is_discovery_enabled()) {
     if (!this->send_discovery_()) {

esphome/components/mqtt/mqtt_component.h

@@ -81,8 +81,6 @@ class MQTTComponent : public Component {
   /// Override setup_ so that we can call send_discovery() when needed.
   void call_setup() override;
 
-  void call_loop() override;
-
   void call_dump_config() override;
 
   /// Send discovery info the Home Assistant, override this.
@@ -133,6 +131,9 @@ class MQTTComponent : public Component {
   /// Internal method for the MQTT client base to schedule a resend of the state on reconnect.
   void schedule_resend_state();
 
+  /// Process pending resend if needed (called by MQTTClientComponent)
+  void process_resend();
+
   /** Send a MQTT message.
    *
    * @param topic The topic.