[time] Build on_time_sync with build_callback_automation (#20441)

tests/component_tests/time/test_triggers.py

@@ -1,5 +1,5 @@
-"""automation.cpp (CronTrigger and SyncTrigger) is only compiled when an
-on_time or on_time_sync automation exists, so the define must follow them."""
+"""automation.cpp (CronTrigger) is only compiled when an on_time automation
+exists, so the define must follow it; on_time_sync needs no class."""
 
 from collections.abc import Callable
 from pathlib import Path
@@ -14,7 +14,7 @@ from esphome.core import CORE
     [
         ("no_triggers.yaml", False),
         ("on_time.yaml", True),
-        ("on_time_sync.yaml", True),
+        ("on_time_sync.yaml", False),
     ],
 )
 def test_triggers_define_follows_automations(

tests/components/time/test-sync.esp8266-ard.yaml

@@ -0,0 +1,8 @@
+wifi:
+  ssid: MySSID
+  password: password1
+
+time:
+  - platform: sntp
+    on_time_sync:
+      - logger.log: Time synchronized