Exposing a type of field operation (flag lists) for search index view
Those flag list operations come from a Views handler; they're applied only to the node entity type in flag_lists_views_data_alter.

The Indexed node isn't a node entity, it's something specific to the search API module (added in search_api_views_views_data). It only contains fields that are indexed, plus any extra stuff search API or contrib modules add on.

I haven't tried it, but you may be able to include the nid in the index, and add a relationship in the View to Content. That would, in theory, give you access to everything that Views knows about for a node.

Failing that, you'll probably have to implement your own Views handler, implement hook_views_data_alter, and find the table whose field handler you need to override (it'll be search_api_index_MACHINE_NAME). The class in includes/flag_lists_handler_field_ops.inc would probably be a good template to start from.