feat(scheduler,conversations,api): cron and schedule in the gateway tz, job runs persisted

tests/test_conversations.py

@@ -4,6 +4,7 @@ import uuid
 from datetime import UTC, datetime
 from pathlib import Path
 from typing import Any
+from zoneinfo import ZoneInfo
 
 import pytest
 from claude_agent_sdk import (
@@ -629,6 +630,9 @@ async def test_schedule_without_scheduler_and_parse_at(world: World) -> None:
     assert parse_at("2026-09-01T10:00:00+02:00") == datetime(
         2026, 9, 1, 8, 0, tzinfo=UTC
     )
+    assert parse_at("2026-09-01T10:00", ZoneInfo("Europe/Warsaw")) == datetime(
+        2026, 9, 1, 8, 0, tzinfo=UTC
+    )
     delta = (parse_at("+15m") - datetime.now(UTC)).total_seconds()
     assert 14 * 60 < delta <= 15 * 60
     with pytest.raises(ValueError, match="Invalid isoformat"):