[core] Inline Mutex on FreeRTOS platforms (ESP32, LibreTiny)

Move FreeRTOS Mutex methods inline into helpers.h, eliminating
duplicate out-of-line definitions in esp32/helpers.cpp and
libretiny/helpers.cpp.

Hot path impact (disassembled from ELF):

| Platform           | Before   | After    | Saved   |
|--------------------|----------|----------|---------|
| ESP32 (Xtensa)     | 1304 B   | 1270 B   | -34 B   |
| BK72xx (ARM M4)    | 1400 B   | 1396 B   | -4 B    |
| RTL87xx (ARM M33)  | 1248 B   | 1246 B   | -2 B    |
| ESP32-C3 (RISC-V)  | 1498 B   | 1494 B   | -4 B    |

GCC generates ISRA clones that hoist the handle_ load into callers
and use tail calls to xQueueSemaphoreTake/xQueueGenericSend.

esphome/components/esp32/helpers.cpp

@@ -20,12 +20,6 @@ bool random_bytes(uint8_t *data, size_t len) {
   return true;
 }
 
-Mutex::Mutex() { handle_ = xSemaphoreCreateMutex(); }
-Mutex::~Mutex() {}
-void Mutex::lock() { xSemaphoreTake(this->handle_, portMAX_DELAY); }
-bool Mutex::try_lock() { return xSemaphoreTake(this->handle_, 0) == pdTRUE; }
-void Mutex::unlock() { xSemaphoreGive(this->handle_); }
-
 // only affects the executing core
 // so should not be used as a mutex lock, only to get accurate timing
 IRAM_ATTR InterruptLock::InterruptLock() { portDISABLE_INTERRUPTS(); }

esphome/components/libretiny/helpers.cpp

@@ -15,12 +15,6 @@ bool random_bytes(uint8_t *data, size_t len) {
   return true;
 }
 
-Mutex::Mutex() { handle_ = xSemaphoreCreateMutex(); }
-Mutex::~Mutex() {}
-void Mutex::lock() { xSemaphoreTake(this->handle_, portMAX_DELAY); }
-bool Mutex::try_lock() { return xSemaphoreTake(this->handle_, 0) == pdTRUE; }
-void Mutex::unlock() { xSemaphoreGive(this->handle_); }
-
 // only affects the executing core
 // so should not be used as a mutex lock, only to get accurate timing
 IRAM_ATTR InterruptLock::InterruptLock() { portDISABLE_INTERRUPTS(); }

esphome/core/helpers.h

@@ -1876,6 +1876,16 @@ class Mutex {
   void lock() {}
   bool try_lock() { return true; }
   void unlock() {}
+#elif defined(USE_ESP32) || defined(USE_LIBRETINY)
+  // FreeRTOS platforms: inline to avoid out-of-line call overhead.
+  Mutex() { handle_ = xSemaphoreCreateMutex(); }
+  ~Mutex() = default;
+  void lock() { xSemaphoreTake(this->handle_, portMAX_DELAY); }
+  bool try_lock() { return xSemaphoreTake(this->handle_, 0) == pdTRUE; }
+  void unlock() { xSemaphoreGive(this->handle_); }
+
+ private:
+  SemaphoreHandle_t handle_;
 #else
   Mutex();
   ~Mutex();
@@ -1884,13 +1894,9 @@ class Mutex {
   void unlock();
 
  private:
-#if defined(USE_ESP32) || defined(USE_LIBRETINY)
-  SemaphoreHandle_t handle_;
-#else
   // d-pointer to store private data on new platforms
   void *handle_;  // NOLINT(clang-diagnostic-unused-private-field)
 #endif
-#endif  // single-threaded check
 };
 
 /** Helper class that wraps a mutex with a RAII-style API.