Deprecation of the home_assistant_start flag of async_initialize_triggers

The dedicated home_assistant_start flag of async_initialize_triggers is deprecated and will be removed in Home Assistant Core 2027.8. During the deprecation period the parameter no longer has any effect.

The flag existed because the homeassistant start trigger was a pseudo trigger: instead of acting like a real trigger, it relied on the caller of the trigger API passing home_assistant_start=True so that async_initialize_triggers would fire the trigger during startup.

The start trigger has been rewritten to work as a real trigger, so the flag is no longer needed. Callers of async_initialize_triggers should simply stop passing home_assistant_start.

To make the new implementation possible, the rewrite adds HomeAssistant.async_add_startup_job, which registers a job to be called after all listeners to EVENT_HOMEASSISTANT_START have executed, but before EVENT_HOMEASSISTANT_STARTED is fired. This mirrors the approach already used for the homeassistant shutdown trigger, and avoids adding yet another core state and event to the already complex relationship between core states and events.

For more details, see core PR 175160.