feature request: Home Assistant Calendar Sync

[disgran]

Checklist

• I checked that this feature has not been requested before
• I checked that this feature is not in the "wontfix / not planned" list
• This feature will benefit the majority of users

Problem Description / Use Case

As a user, I want to keep BetterShift running locally without exposing a public calendar,
but still synchronize my shifts with my Home Assistant instance for personal automation, dashboards, and reminders.

Proposed Solution

Add support for Home Assistant calendar sync alongside existing external calendars (Google Calendar, iCal).
Control the functionality via environment variables:

Enable Home Assistant sync (true/false)
HA_SYNC_ENABLED=
Base URL of the Home Assistant instance
HA_URL=
Long-lived access token for authentication
HA_TOKEN=
Target calendar ID in Home Assistant
HA_CALENDAR_ID=

When enabled, each shift would automatically create or update events in the specified Home Assistant calendar,
and optionally remove events for deleted shifts.
This allows private, local usage of BetterShift while keeping calendars updated in Home Assistant.