updated test

 WITH RECURSIVE partition_hierarchy AS (

    -- Start with the direct children of the parent table

    SELECT 

        child.oid AS partition_oid,

        child.relname AS partition_name,

        parent.relname AS parent_name,

        nsp.nspname AS schema_name

    FROM 

        pg_inherits i

    JOIN 

        pg_class child ON i.inhrelid = child.oid

    JOIN 

        pg_class parent ON i.inhparent = parent.oid

    JOIN 

        pg_namespace nsp ON child.relnamespace = nsp.oid

    WHERE 

        parent.relname = '<your_parent_table_name>' -- Replace with your parent table name

        AND nsp.nspname = '<your_schema_name>'     -- Replace with your schema name

    UNION ALL

    -- Recursively find children of the current partitions

    SELECT 

        child.oid AS partition_oid,

        child.relname AS partition_name,

        parent.relname AS parent_name,

        nsp.nspname AS schema_name

    FROM 

        pg_inherits i

    JOIN 

        pg_class child ON i.inhrelid = child.oid

        JOIN pg_class parent ON i.inhparent = parent.oid

        JOIN pg_namespace nsp ON child.relnamespace = nsp.oid

        JOIN partition_hierarchy ph ON parent.oid = ph.partition_oid

)

SELECT 

    ph.schema_name || '.' || ph.partition_name AS partition_table,

    st.last_autovacuum,

    st.last_autoanalyze,

    st.n_dead_tup,

    st.n_mod_since_analyze,

    st.n_live_tup

FROM 

    partition_hierarchy ph

LEFT JOIN 

    pg_stat_user_tables st 

    ON ph.schema_name || '.' || ph.partition_name = st.schemaname || '.' || st.relname

ORDER BY 

    st.last_autoanalyze NULLS FIRST,  -- Prioritize tables never autoanalyzed

    st.n_mod_since_analyze DESC;     -- Sort by modifications