Add runtime_stats component for performance debugging and analysis (#9386)

Co-authored-by: Keith Burzinski <kbx81x@gmail.com>

esphome/core/application.cpp

@@ -4,6 +4,9 @@
 #include "esphome/core/hal.h"
 #include <algorithm>
 #include <ranges>
+#ifdef USE_RUNTIME_STATS
+#include "esphome/components/runtime_stats/runtime_stats.h"
+#endif
 
 #ifdef USE_STATUS_LED
 #include "esphome/components/status_led/status_led.h"
@@ -141,6 +144,14 @@ void Application::loop() {
   this->in_loop_ = false;
   this->app_state_ = new_app_state;
 
+#ifdef USE_RUNTIME_STATS
+  // Process any pending runtime stats printing after all components have run
+  // This ensures stats printing doesn't affect component timing measurements
+  if (global_runtime_stats != nullptr) {
+    global_runtime_stats->process_pending_stats(last_op_end_time);
+  }
+#endif
+
   // Use the last component's end time instead of calling millis() again
   auto elapsed = last_op_end_time - this->last_loop_;
   if (elapsed >= this->loop_interval_ || HighFrequencyLoopRequester::is_high_frequency()) {