[api] Keep add_item_front out-of-line to avoid bloating cold callers

add_item_front is only called from on_shutdown and check_keepalive_
which are cold paths. Keeping it out-of-line prevents inlining
push_back into those callers.

esphome/components/api/api_connection.cpp

@@ -2072,6 +2072,14 @@ void APIConnection::on_fatal_error() {
   this->flags_.remove = true;
 }
 
+void APIConnection::DeferredBatch::add_item_front(EntityBase *entity, uint8_t message_type, uint8_t estimated_size) {
+  // Swap to front avoids expensive vector::insert which shifts all elements
+  this->items.push_back({entity, message_type, estimated_size, AUX_DATA_UNUSED});
+  if (this->items.size() > 1) {
+    std::swap(this->items.front(), this->items.back());
+  }
+}
+
 bool APIConnection::send_message_smart_(EntityBase *entity, uint8_t message_type, uint8_t estimated_size,
                                         uint8_t aux_data_index) {
   if (this->should_send_immediately_(message_type) && this->helper_->can_write_without_blocking()) {

esphome/components/api/api_connection.h

@@ -659,13 +659,8 @@ class APIConnection final : public APIServerConnectionBase {
       this->items.push_back({entity, message_type, estimated_size, aux_data_index});
     }
     // Add item to the front of the batch (for high priority messages like ping)
-    void add_item_front(EntityBase *entity, uint8_t message_type, uint8_t estimated_size) {
-      // Swap to front avoids expensive vector::insert which shifts all elements
-      this->items.push_back({entity, message_type, estimated_size, AUX_DATA_UNUSED});
-      if (this->items.size() > 1) {
-        std::swap(this->items.front(), this->items.back());
-      }
-    }
+    // Out-of-line: called from cold paths (on_shutdown, check_keepalive_)
+    void add_item_front(EntityBase *entity, uint8_t message_type, uint8_t estimated_size);
 
     // Clear all items
     void clear() {