[api] Fix compilation error with char* lambdas in HomeAssistant services (#9638)

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

tests/integration/fixtures/api_string_lambda.yaml

@@ -60,5 +60,28 @@ api:
             data:
               value: !lambda 'return input_float;'
 
+    # Service that tests char* lambda functionality (e.g., from itoa or sprintf)
+    - action: test_char_ptr_lambda
+      variables:
+        input_number: int
+        input_string: string
+      then:
+        # Log the input to verify service was called
+        - logger.log:
+            format: "Service called with number for char* test: %d"
+            args: [input_number]
+
+        # Test that char* lambdas work correctly
+        # This would fail in issue #9628 with "invalid conversion from 'char*' to 'long long unsigned int'"
+        - homeassistant.event:
+            event: esphome.test_char_ptr_lambda
+            data:
+              # Test snprintf returning char*
+              decimal_value: !lambda 'static char buffer[20]; snprintf(buffer, sizeof(buffer), "%d", input_number); return buffer;'
+              # Test strdup returning char* (dynamically allocated)
+              string_copy: !lambda 'return strdup(input_string.c_str());'
+              # Test string literal (const char*)
+              literal: !lambda 'return "test literal";'
+
 logger:
   level: DEBUG

tests/integration/test_api_string_lambda.py

@@ -19,15 +19,17 @@ async def test_api_string_lambda(
     """Test TemplatableStringValue works with lambdas that return different types."""
     loop = asyncio.get_running_loop()
 
-    # Track log messages for all three service calls
+    # Track log messages for all four service calls
     string_called_future = loop.create_future()
     int_called_future = loop.create_future()
     float_called_future = loop.create_future()
+    char_ptr_called_future = loop.create_future()
 
     # Patterns to match in logs - confirms the lambdas compiled and executed
     string_pattern = re.compile(r"Service called with string: STRING_FROM_LAMBDA")
     int_pattern = re.compile(r"Service called with int: 42")
     float_pattern = re.compile(r"Service called with float: 3\.14")
+    char_ptr_pattern = re.compile(r"Service called with number for char\* test: 123")
 
     def check_output(line: str) -> None:
         """Check log output for expected messages."""
@@ -37,6 +39,8 @@ async def test_api_string_lambda(
             int_called_future.set_result(True)
         if not float_called_future.done() and float_pattern.search(line):
             float_called_future.set_result(True)
+        if not char_ptr_called_future.done() and char_ptr_pattern.search(line):
+            char_ptr_called_future.set_result(True)
 
     # Run with log monitoring
     async with (
@@ -65,17 +69,28 @@ async def test_api_string_lambda(
         )
         assert float_service is not None, "test_float_lambda service not found"
 
-        # Execute all three services to test different lambda return types
+        char_ptr_service = next(
+            (s for s in services if s.name == "test_char_ptr_lambda"), None
+        )
+        assert char_ptr_service is not None, "test_char_ptr_lambda service not found"
+
+        # Execute all four services to test different lambda return types
         client.execute_service(string_service, {"input_string": "STRING_FROM_LAMBDA"})
         client.execute_service(int_service, {"input_number": 42})
         client.execute_service(float_service, {"input_float": 3.14})
+        client.execute_service(
+            char_ptr_service, {"input_number": 123, "input_string": "test_string"}
+        )
 
         # Wait for all service log messages
         # This confirms the lambdas compiled successfully and executed
         try:
             await asyncio.wait_for(
                 asyncio.gather(
-                    string_called_future, int_called_future, float_called_future
+                    string_called_future,
+                    int_called_future,
+                    float_called_future,
+                    char_ptr_called_future,
                 ),
                 timeout=5.0,
             )