[esp32_ble_server] Fix set_value action with by-reference triggers (#17156)

esphome/components/esp32_ble_server/ble_server_automations.h

@@ -77,13 +77,15 @@ template<typename... Ts> class BLECharacteristicSetValueAction : public Action<T
     // Set initial value
     this->parent_->set_value(this->buffer_.value(x...));
     // Set the listener for read events
-    this->parent_->on_read([this, x...](uint16_t id) {
+    // ``mutable`` keeps by-copy captures non-const for triggers passing args by reference
+    // (e.g. climate on_control's ClimateCall&). See #17142.
+    this->parent_->on_read([this, x...](uint16_t id) mutable {
       // Set the value of the characteristic every time it is read
       this->parent_->set_value(this->buffer_.value(x...));
     });
     // Set the listener in the global manager so only one BLECharacteristicSetValueAction is set for each characteristic
     BLECharacteristicSetValueActionManager::get_instance()->set_listener(
-        this->parent_, [this, x...]() { this->parent_->set_value(this->buffer_.value(x...)); });
+        this->parent_, [this, x...]() mutable { this->parent_->set_value(this->buffer_.value(x...)); });
   }
 
  protected:

tests/components/esp32_ble_server/common.yaml

@@ -77,3 +77,34 @@ esp32_ble_server:
                   id: test_change_descriptor
                   value:
                     data: [0x01, 0x02, 0x03]
+
+# Regression test for #17142: the set_value action used from a trigger that passes
+# its argument by reference (climate on_control supplies ClimateCall&) previously
+# failed to compile.
+sensor:
+  - platform: template
+    id: ble_test_temp
+    lambda: "return 20.0;"
+
+output:
+  - platform: template
+    id: ble_test_output
+    type: float
+    write_action:
+      - logger.log: "out"
+
+climate:
+  - platform: pid
+    name: "BLE Test Climate"
+    id: ble_test_climate
+    sensor: ble_test_temp
+    default_target_temperature: 20
+    heat_output: ble_test_output
+    control_parameters:
+      kp: 0.1
+      ki: 0.001
+      kd: 0.1
+    on_control:
+      - ble_server.characteristic.set_value:
+          id: test_notify_characteristic
+          value: !lambda "return std::vector<uint8_t>{0, 1, 2};"