query that returns a tree in json (full tree from root or subtree from node n) with RCTE

get_tree.sql

CREATE OR REPLACE FUNCTION build_tree(parent_id INTEGER DEFAULT NULL)
RETURNS JSONB AS $$
DECLARE
    result JSONB;
    count INTEGER;
BEGIN
    SELECT COUNT(*)
    INTO count
    FROM nodes n
    WHERE n.parent_id IS NOT DISTINCT FROM $1;
    
    WITH children AS (
        SELECT 
            n.id,
            n.name,
            build_tree(n.id) as child_tree
        FROM nodes n
        WHERE n.parent_id IS NOT DISTINCT FROM $1
    )
    SELECT COALESCE(
        jsonb_agg(
            jsonb_build_object(
                'id', name,
                'children', COALESCE(child_tree, '[]'::jsonb)
            )
        ),
        '[]'::jsonb
    )
    INTO result
    FROM children;

    RETURN result;
END;
$$ LANGUAGE plpgsql;