How to define and query in case of table with Mutually exclusive one-to-many relationships
It will be something like:

SELECT e.index,
       e.entityname,
       COALESCE(a1.AggregateName, a2.AggregateName, a3.AggregateName) AggregateName,
       COALESCE(c2.CountryName, c3.CountryName) CountryName, 
       r3.Region,
       e.Value
FROM Entity e
-- when idAggregate_fkey is specified
LEFT JOIN Aggregate a1 ON a1.idAggregate = e.idAggregate_fkey
-- when idCountry_fkey is specified
LEFT JOIN Country c2 ON c2.idCountry = e.idCountry_fkey
LEFT JOIN Aggregate_to_Country ac2 ON ac2.idCountry_fkey = e.idCountry_fkey
LEFT JOIN Aggregate a2 ON a2.idAggregate = ac2.idAggregate_fkey
-- when idRegion_fkey is specified
LEFT JOIN Region r3 ON r3.idRegion = e.idRegion_fkey
LEFT JOIN Country c3 ON c3.idCountry = r3.idCountry_fkey
LEFT JOIN Aggregate_to_Country ac3 ON ac3.idCountry_fkey = c3.idCountry_fkey
LEFT JOIN Aggregate a3 ON a3.idAggregate = ac3.idAggregate_fkey



Check join order and conditions for each branch - I may make a mistake.
Check if some joins may be INNER.