The recursive part of the query builds a table r that has all objects at all levels. This is done by iteratively joining the table itself with the geo_objects_attributes and geo_objects tables. The top level region is added in the first part of the union (select 1) and then the geo_objects_attributes and geo_objects tables are joined with the table r itself. This is done for all levels of the hierarchy. In the end, the result is simply joined with the geo_polygons table.

with recursive r as (
  select root.id as id, root.name as name, root.level as level, root.parent_id as parent_id, root.id as parent_name, 1 as path_len
  from geo_objects root
  where root.parent_id is null
  union all
  select a.id as id, a.name as name, a.level as level, a.parent_id as parent_id, r.parent_name as parent_name, path_len + 1 as path_len
  from geo_objects a
  join r on a.parent_id = r.id
)
select r.id, r.name, r.level, r.parent_id, r.parent_name, r.path_len, g.id as geo_polygon_id, ST_AsGeoJSON(geo_polygon) as geo_polygon
from r
left outer join geo_polygons g on r.id = g.object_id
where r.level = 4
order by r.id;