[api] De-duplicate iterator batch processing in APIConnection::loop()

Replace the process_iterator_batch_ template (instantiated separately
for ListEntitiesIterator and InitialStateIterator) with a single
non-template method taking a ComponentIterator& base class reference.

Both iterators inherit from ComponentIterator, and the template only
called completed() and advance() which are both base class methods.
The two template instantiations generated ~160 bytes of duplicate code
in APIConnection::loop(). The single non-template version is 79 bytes,
saving 61 bytes net flash and removing 140 bytes of cold
connect/reconnect code from the hot loop path.

Also move the duplicated completed() method from ListEntitiesIterator
and InitialStateIterator to the ComponentIterator base class where
state_ is defined.

esphome/components/api/api_connection.cpp

@@ -283,6 +283,20 @@ void APIConnection::loop() {
 #endif
 }
 
+void APIConnection::process_iterator_batch_(ComponentIterator &iterator) {
+  size_t initial_size = this->deferred_batch_.size();
+  size_t max_batch = this->get_max_batch_size_();
+  while (!iterator.completed() && (this->deferred_batch_.size() - initial_size) < max_batch) {
+    iterator.advance();
+  }
+
+  // If the batch is full, process it immediately
+  // Note: iterator.advance() already calls schedule_batch_() via schedule_message_()
+  if (this->deferred_batch_.size() >= max_batch) {
+    this->process_batch_();
+  }
+}
+
 bool APIConnection::send_disconnect_response_() {
   // remote initiated disconnect_client
   // don't close yet, we still need to send the disconnect response

esphome/components/api/api_connection.h

@@ -364,20 +364,9 @@ class APIConnection final : public APIServerConnectionBase {
     return this->client_supports_api_version(1, 14) ? MAX_INITIAL_PER_BATCH : MAX_INITIAL_PER_BATCH_LEGACY;
   }
 
-  // Helper method to process multiple entities from an iterator in a batch
-  template<typename Iterator> void process_iterator_batch_(Iterator &iterator) {
-    size_t initial_size = this->deferred_batch_.size();
-    size_t max_batch = this->get_max_batch_size_();
-    while (!iterator.completed() && (this->deferred_batch_.size() - initial_size) < max_batch) {
-      iterator.advance();
-    }
-
-    // If the batch is full, process it immediately
-    // Note: iterator.advance() already calls schedule_batch_() via schedule_message_()
-    if (this->deferred_batch_.size() >= max_batch) {
-      this->process_batch_();
-    }
-  }
+  // Helper method to process multiple entities from an iterator in a batch.
+  // Takes ComponentIterator base class reference to avoid duplicate template instantiations.
+  void process_iterator_batch_(ComponentIterator &iterator);
 
 #ifdef USE_BINARY_SENSOR
   static uint16_t try_send_binary_sensor_state(EntityBase *entity, APIConnection *conn, uint32_t remaining_size);

esphome/components/api/list_entities.h

@@ -94,7 +94,6 @@ class ListEntitiesIterator : public ComponentIterator {
   bool on_update(update::UpdateEntity *entity) override;
 #endif
   bool on_end() override;
-  bool completed() { return this->state_ == IteratorState::NONE; }
 
  protected:
   APIConnection *client_;

esphome/components/api/subscribe_state.h

@@ -88,7 +88,6 @@ class InitialStateIterator : public ComponentIterator {
 #ifdef USE_UPDATE
   bool on_update(update::UpdateEntity *entity) override;
 #endif
-  bool completed() { return this->state_ == IteratorState::NONE; }
 
  protected:
   APIConnection *client_;

esphome/core/component_iterator.h

@@ -26,6 +26,7 @@ class ComponentIterator {
  public:
   void begin(bool include_internal = false);
   void advance();
+  bool completed() const { return this->state_ == IteratorState::NONE; }
   virtual bool on_begin();
 #ifdef USE_BINARY_SENSOR
   virtual bool on_binary_sensor(binary_sensor::BinarySensor *binary_sensor) = 0;