The Auto-Sync schedule board was detecting its own automations by
checking `group_name === 'Playlist Auto-Sync' || name.startsWith('Auto-Sync:')`.
That's fragile — renaming the row from the Automations page silently
hands ownership back to the read-only Automation Pipelines tab and the
board stops managing it.
This commit replaces the string convention with an explicit
`automations.owned_by` TEXT column:
- Migration `_add_automation_owned_by_column` adds the column and
backfills `'auto_sync'` for existing rows that match the legacy
`group_name`/`name`-prefix pattern, so users running the migration
don't lose their schedules.
- `database.create_automation` and `database.update_automation` accept
`owned_by` (the latter via its `allowed` kwarg set).
- `core/automation/api.py` forwards `owned_by` on both POST and PUT.
Missing field is left as None, preserving today's behavior for every
caller that doesn't opt in.
- The Auto-Sync schedule board posts `owned_by: 'auto_sync'` and the
detection helper now prefers that signal, falling back to the legacy
name/group convention so any hand-rolled rows still show up.
Tests: three new cases in `tests/automation/test_automation_api.py`
covering create-with-owned-by, create-without (defaults to None), and
update set/clear. The fake DB grew the matching kwarg.
9b086c5a65