[template] Add regression tests for lambdas with captures (PR #11555)

tests/components/template/common-base.yaml

@@ -9,6 +9,27 @@ esphome:
         id: template_sens
         state: !lambda "return 42.0;"
 
+    # Test C++ API: set_template() with stateless lambda (no captures)
+    - lambda: |-
+        id(template_sens).set_template([]() -> esphome::optional<float> {
+          return 123.0f;
+        });
+
+    # Test C++ API: set_template() with stateful lambda (with captures)
+    # This is the regression test for issue #11555
+    - lambda: |-
+        float captured_value = 456.0f;
+        id(template_sens).set_template([captured_value]() -> esphome::optional<float> {
+          return captured_value;
+        });
+
+    # Test C++ API: set_template() with more complex capture
+    - lambda: |-
+        auto sensor_id = id(template_sens);
+        id(template_number).set_template([sensor_id]() -> esphome::optional<float> {
+          return sensor_id->state * 2.0f;
+        });
+
     - datetime.date.set:
         id: test_date
         date:
@@ -215,6 +236,7 @@ cover:
 
 number:
   - platform: template
+    id: template_number
     name: "Template number"
     optimistic: true
     min_value: 0