[core] Flatten single-callsite vector realloc functions (#13970)

esphome/components/api/api_connection.h

@@ -541,6 +541,8 @@ class APIConnection final : public APIServerConnectionBase {
                   uint8_t aux_data_index = AUX_DATA_UNUSED);
     // 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);
+    // Single push_back site to avoid duplicate _M_realloc_insert instantiation
+    void push_item(const BatchItem &item);
 
     // Clear all items
     void clear() {