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AFAIK type in index already has partent chain path with ids - but for denormalization you can try to include StartPgeId field or so in indexable fields.
SearchClient.Instance.Conventions.ForInstancesOf<PageData>().IncludeField(x => x.StartPageId());
..
public static string StartPageId(this PageData content)
{
// travel by ParentLink to find top most parent (StartPage) or fetch StartPage from repository directly
}
Then you can use this field to query for content for specific site.
How do I fetch what startpage (in a multisite) a document belongs to?.
I want to index all mediadata with its belonging startpage id so that I can filter this site per site.