Do not leave out the referential constraints (based on adjacency list design)

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WITH keys as (select 
o.conname,
(select nspname from pg_namespace where oid=m.relnamespace) as key_schema,
m.relname as key_table, 
m.oid as key_table_oid,
o.conkey AS key_col
from pg_constraint o inner join pg_class c on c.oid = o.conrelid
inner join pg_class m on m.oid = o.conrelid
where o.contype in ('u','p','f')  and o.conrelid in (select oid from pg_class c where c.relkind = 'r')),
keys_unnest as (select conname, key_schema, key_table, key_table_oid, key_col, key_col_num, ordin
from keys, unnest(keys.key_col) with ordinality as k(key_col_num, ordin)),
keys_with_names as (select key_schema as table_schema, key_table as table_name, a_key.attname as column_name
from keys_unnest k inner join pg_attribute a_key on k.key_col_num = a_key.attnum and k.key_table_oid = a_key.attrelid and a_key.attisdropped = false),
surrogate_key AS (SELECT c.table_schema, c.table_name , c.column_name
FROM information_schema.columns c
LEFT JOIN information_schema.domains d USING (domain_schema, domain_name)
INNER JOIN information_schema.schemata s
ON c.table_schema=s.schema_name
WHERE  (coalesce (c.column_default, d.domain_default) ILIKE '%nextval%'  OR c.is_identity='YES')
AND (c.table_schema = 'public'
OR s.schema_owner<>'postgres'))

SELECT table_schema, table_name, column_name,  data_type, character_maximum_length
FROM INFORMATION_SCHEMA.columns AS c INNER JOIN INFORMATION_SCHEMA.tables USING (table_schema, table_name)
WHERE column_name~*'parent'
AND table_type='BASE TABLE' 
AND NOT EXISTS (SELECT *
FROM keys_with_names AS kwn
WHERE kwn.table_schema=c.table_schema
AND kwn.table_name=c.table_name
AND kwn.column_name=c.column_name)
AND NOT EXISTS (SELECT *
FROM surrogate_key AS sk
WHERE sk.table_schema=c.table_schema
AND sk.table_name=c.table_name
AND sk.column_name=c.column_name)
AND table_schema NOT IN (SELECT schema_name
FROM INFORMATION_SCHEMA.schemata
WHERE schema_name<>'public' AND
schema_owner='postgres' AND schema_name IS NOT NULL)
ORDER BY table_type, table_schema, table_name, ordinal_position;