Use new ISO format for compilation_time in API DeviceInfo

Change the API's DeviceInfo response to use the new ISO 8601 format
with timezone for compilation_time field by calling get_build_time_string()
instead of get_compilation_time_ref().

Update the placeholder build_info_data.h to match the new format.

Update integration test to expect the new format for compilation_time.

esphome/components/api/api_connection.cpp

@@ -1472,7 +1472,10 @@ bool APIConnection::send_device_info_response(const DeviceInfoRequest &msg) {
 
   resp.set_esphome_version(ESPHOME_VERSION_REF);
 
-  resp.set_compilation_time(App.get_compilation_time_ref());
+  // Stack buffer for build time string
+  char build_time_str[Application::BUILD_TIME_STR_SIZE];
+  App.get_build_time_string(build_time_str);
+  resp.set_compilation_time(StringRef(build_time_str));
 
   // Manufacturer string - define once, handle ESP8266 PROGMEM separately
 #if defined(USE_ESP8266) || defined(USE_ESP32)

esphome/core/build_info_data.h

@@ -7,4 +7,4 @@
 
 #define ESPHOME_CONFIG_HASH 0x12345678U  // NOLINT
 #define ESPHOME_BUILD_TIME 1700000000    // NOLINT
-static const char ESPHOME_BUILD_TIME_STR[] = "Jan 01 2024, 00:00:00";
+static const char ESPHOME_BUILD_TIME_STR[] = "2024-01-01 00:00:00 +0000";

tests/integration/test_build_info.py

@@ -26,7 +26,7 @@ async def test_build_info(
         assert device_info.name == "build-info-test"
 
         # Verify compilation_time from device_info is present and parseable
-        # The format is "Mon DD YYYY, HH:MM:SS" (e.g., "Dec 13 2024, 15:30:00")
+        # The format is ISO 8601 with timezone: "YYYY-MM-DD HH:MM:SS +ZZZZ"
         compilation_time = device_info.compilation_time
         assert compilation_time is not None