[core] Trim scheduler freelist of post-boot peak 10s after setup

Boot churn (component init, first sensor reads, retries) inflates the freelist
beyond the steady-state high-water mark. Without a one-shot trim that peak
would be retained forever. Adds Scheduler::trim_freelist() and schedules it
from Application::setup() to fire SCHEDULER_FREELIST_TRIM_DELAY_MS (10s) after
setup completes -- well past the bulk of post-setup async work.

Items currently in items_/to_add_/defer_queue_ are untouched; only the
freelist's recycled items are deleted. Post-trim, the freelist regrows to
the new (post-startup) high-water mark.

esphome/core/application.cpp

@@ -25,6 +25,10 @@ namespace esphome {
 
 static const char *const TAG = "app";
 
+// Delay after setup() finishes before trimming the scheduler freelist of its post-boot peak.
+// 10 s is well past the bulk of post-setup async work (Wi-Fi/MQTT connects, first-read latency).
+static constexpr uint32_t SCHEDULER_FREELIST_TRIM_DELAY_MS = 10000;
+
 // Helper function for insertion sort of components by priority
 // Using insertion sort instead of std::stable_sort saves ~1.3KB of flash
 // by avoiding template instantiations (std::rotate, std::stable_sort, lambdas)
@@ -112,6 +116,9 @@ void Application::setup() {
 
   ESP_LOGI(TAG, "setup() finished successfully!");
 
+  // Trim the scheduler freelist of its post-boot peak once startup churn settles.
+  this->scheduler.set_timeout(this, SCHEDULER_FREELIST_TRIM_DELAY_MS, [this]() { this->scheduler.trim_freelist(); });
+
 #ifdef USE_SETUP_PRIORITY_OVERRIDE
   // Clear setup priority overrides to free memory
   clear_setup_priority_overrides();

esphome/core/scheduler.cpp

@@ -899,6 +899,28 @@ void Scheduler::recycle_item_main_loop_(SchedulerItem *item) {
 #endif
 }
 
+void Scheduler::trim_freelist() {
+  LockGuard guard{this->lock_};
+  SchedulerItem *item = this->scheduler_item_pool_head_;
+  size_t freed = 0;
+  while (item != nullptr) {
+    SchedulerItem *next = item->next_free;
+    delete item;
+#ifdef ESPHOME_DEBUG_SCHEDULER
+    this->debug_live_items_--;
+#endif
+    item = next;
+    freed++;
+  }
+  this->scheduler_item_pool_head_ = nullptr;
+  this->scheduler_item_pool_size_ = 0;
+#ifdef ESPHOME_DEBUG_SCHEDULER
+  ESP_LOGD(TAG, "Freelist trimmed (%zu items freed)", freed);
+#else
+  (void) freed;
+#endif
+}
+
 #ifdef ESPHOME_DEBUG_SCHEDULER
 void Scheduler::debug_log_timer_(const SchedulerItem *item, NameType name_type, const char *static_name,
                                  uint32_t hash_or_id, SchedulerItem::Type type, uint32_t delay, uint64_t now) {

esphome/core/scheduler.h

@@ -132,6 +132,13 @@ class Scheduler {
   // @return Timestamp of the last item that ran, or `now` unchanged if none ran.
   uint32_t call(uint32_t now);
 
+  // Free every SchedulerItem currently sitting in the recycle freelist. Items in
+  // items_/to_add_/defer_queue_ are untouched. Intended to claim the post-boot
+  // peak: boot churn (component setup, first sensor reads, retries) inflates the
+  // freelist beyond what steady-state needs, and without a one-shot trim that
+  // peak would be retained forever.
+  void trim_freelist();
+
   // Move items from to_add_ into the main heap.
   // IMPORTANT: This method should only be called from the main thread (loop task).
   // Inlined: the fast path (nothing to add) is just an atomic load / empty check.