SELECT con.conname      AS constraint_name,
       rel.relname      AS table_name,
       array_agg(col.attname) AS columns
FROM   pg_constraint con
JOIN   pg_class rel   ON rel.oid = con.conrelid
JOIN   pg_namespace nsp ON nsp.oid = con.connamespace
JOIN   pg_attribute col ON col.attrelid = con.conrelid
                        AND col.attnum = ANY (con.conkey)
WHERE  con.contype = 'u'   -- only UNIQUE constraints
  AND  nsp.nspname = 'public'  -- your schema (adjust if needed)
GROUP BY con.conname, rel.relname
ORDER BY rel.relname, con.conname;