Permanently deletes the product group. This is a hard delete: the record is removed and cannot be recovered. Returns 404 if no group with that ID belongs to the company.

Deleting a group ripples to everything that referenced it: • Products in this group are un-grouped — their group becomes empty. The products themselves are not deleted. • The group is dropped from any menus that featured it as a collection. • Any price tier that targeted or excluded this group has that condition removed, which changes which products those price tiers apply to.

Required permission: settings_permissions_product_groups.