diff --git a/esphome/components/api/api_connection.cpp b/esphome/components/api/api_connection.cpp
index 3d0ca4eb31..9b27eec753 100644
--- a/esphome/components/api/api_connection.cpp
+++ b/esphome/components/api/api_connection.cpp
@@ -180,7 +180,8 @@ void APIConnection::loop() {
       on_fatal_error();
       ESP_LOGW(TAG, "%s is unresponsive; disconnecting", this->get_client_combined_info().c_str());
     }
-  } else if (now - this->last_traffic_ > KEEPALIVE_TIMEOUT_MS) {
+  } else if (now - this->last_traffic_ > KEEPALIVE_TIMEOUT_MS && !this->flags_.remove) {
+    // Only send ping if we're not disconnecting
     ESP_LOGVV(TAG, "Sending keepalive PING");
     this->flags_.sent_ping = this->send_message(PingRequest());
     if (!this->flags_.sent_ping) {
@@ -1625,8 +1626,15 @@ void APIConnection::DeferredBatch::add_item(EntityBase *entity, MessageCreator c
 
 void APIConnection::DeferredBatch::add_item_front(EntityBase *entity, MessageCreator creator, uint8_t message_type,
                                                   uint8_t estimated_size) {
-  // Insert at front for high priority messages (no deduplication check)
-  items.insert(items.begin(), BatchItem(entity, std::move(creator), message_type, estimated_size));
+  // Add high priority message and swap to front
+  // This avoids expensive vector::insert which shifts all elements
+  // Note: We only ever have one high-priority message at a time (ping OR disconnect)
+  // If we're disconnecting, pings are blocked, so this simple swap is sufficient
+  items.emplace_back(entity, std::move(creator), message_type, estimated_size);
+  if (items.size() > 1) {
+    // Swap the new high-priority item to the front
+    std::swap(items.front(), items.back());
+  }
 }
 
 bool APIConnection::schedule_batch_() {
diff --git a/esphome/components/opentherm/output/output.cpp b/esphome/components/opentherm/output/output.cpp
index f820dc76f1..486aa0d4e7 100644
--- a/esphome/components/opentherm/output/output.cpp
+++ b/esphome/components/opentherm/output/output.cpp
@@ -10,7 +10,7 @@ void opentherm::OpenthermOutput::write_state(float state) {
   ESP_LOGD(TAG, "Received state: %.2f. Min value: %.2f, max value: %.2f", state, min_value_, max_value_);
   this->state = state < 0.003 && this->zero_means_zero_
                     ? 0.0
-                    : clamp(lerp(state, min_value_, max_value_), min_value_, max_value_);
+                    : clamp(std::lerp(min_value_, max_value_, state), min_value_, max_value_);
   this->has_state_ = true;
   ESP_LOGD(TAG, "Output %s set to %.2f", this->id_, this->state);
 }
diff --git a/esphome/components/servo/servo.cpp b/esphome/components/servo/servo.cpp
index b8546d345c..b4511de2d0 100644
--- a/esphome/components/servo/servo.cpp
+++ b/esphome/components/servo/servo.cpp
@@ -88,9 +88,9 @@ void Servo::internal_write(float value) {
   value = clamp(value, -1.0f, 1.0f);
   float level;
   if (value < 0.0) {
-    level = lerp(-value, this->idle_level_, this->min_level_);
+    level = std::lerp(this->idle_level_, this->min_level_, -value);
   } else {
-    level = lerp(value, this->idle_level_, this->max_level_);
+    level = std::lerp(this->idle_level_, this->max_level_, value);
   }
   this->output_->set_level(level);
   this->current_value_ = value;
diff --git a/tests/components/captive_portal/test.bk72xx-ard.yaml b/tests/components/captive_portal/test.bk72xx-ard.yaml
new file mode 100644
index 0000000000..dade44d145
--- /dev/null
+++ b/tests/components/captive_portal/test.bk72xx-ard.yaml
@@ -0,0 +1 @@
+<<: !include common.yaml