[api] Move schedule_message_front_ out-of-line to avoid cold path bloat

schedule_message_front_ is only called from cold paths (on_shutdown,
check_keepalive_). Moving it out-of-line prevents add_item_front and
push_back from being inlined into those callers.

esphome/components/api/api_connection.cpp

@@ -2072,6 +2072,11 @@ void APIConnection::on_fatal_error() {
   this->flags_.remove = true;
 }
 
+bool APIConnection::schedule_message_front_(EntityBase *entity, uint8_t message_type, uint8_t estimated_size) {
+  this->deferred_batch_.add_item_front(entity, message_type, estimated_size);
+  return this->schedule_batch_();
+}
+
 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

@@ -797,10 +797,8 @@ class APIConnection final : public APIServerConnectionBase {
   }
 
   // Helper function to schedule a high priority message at the front of the batch
-  bool schedule_message_front_(EntityBase *entity, uint8_t message_type, uint8_t estimated_size) {
-    this->deferred_batch_.add_item_front(entity, message_type, estimated_size);
-    return this->schedule_batch_();
-  }
+  // Out-of-line: callers (on_shutdown, check_keepalive_) are cold paths
+  bool schedule_message_front_(EntityBase *entity, uint8_t message_type, uint8_t estimated_size);
 
   // Helper function to log client messages with name and peername
   void log_client_(int level, const LogString *message);