Add Baby Tracker client and Home Assistant integration

Python client for the Baby Tracker sync server, reverse engineered from
the Android app (4.53), and a HACS-installable Home Assistant integration
built on it. Each baby gets a log calendar and summary sensors, and actions
add entries that sync back to the group.

Reading has been run against the real server. Uploading and running inside
real Home Assistant have not.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/ha_stubs/homeassistant/components/calendar/__init__.py

@@ -0,0 +1,24 @@
+from dataclasses import dataclass
+from datetime import datetime
+from typing import Optional
+
+from ...exceptions import HomeAssistantError
+
+
+@dataclass
+class CalendarEvent:
+    start: datetime
+    end: datetime
+    summary: str
+    description: Optional[str] = None
+    uid: Optional[str] = None
+
+    def __post_init__(self):
+        if self.start.tzinfo is None or self.end.tzinfo is None:
+            raise HomeAssistantError("Expected all values to have a timezone")
+        if self.end <= self.start:
+            raise HomeAssistantError("Expected end time to be after start time")
+
+
+class CalendarEntity:
+    pass