[api] Inline push_item to allow push_back to be inlined into caller

The out-of-line push_item with __attribute__((flatten)) inlined
push_back's callees into push_item, but push_item itself remained
a function call barrier. Moving push_item inline lets the compiler
inline push_back into the actual call sites (add_item, add_item_front).

esphome/components/api/api_connection.cpp

@@ -2072,8 +2072,6 @@ void APIConnection::on_fatal_error() {
   this->flags_.remove = true;
 }
 
-void __attribute__((flatten)) APIConnection::DeferredBatch::push_item(const BatchItem &item) { items.push_back(item); }
-
 void APIConnection::DeferredBatch::add_item(EntityBase *entity, uint8_t message_type, uint8_t estimated_size,
                                             uint8_t aux_data_index) {
   // Check if we already have a message of this type for this entity

esphome/components/api/api_connection.h

@@ -647,10 +647,7 @@ 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);
-    // Out-of-line with flatten: inlines push_back callees into push_item,
-    // but keeps push_item itself as a call from add_item. This prevents
-    // the compiler from bloating add_item's dedup loop and degrading icache.
-    void push_item(const BatchItem &item);
+    void push_item(const BatchItem &item) { items.push_back(item); }
 
     // Clear all items
     void clear() {