Actually just ran that setup, statement logging set to all rebooted the DB and nothing else connecting to it (no data in the DB besides the public schema on the default postgres empty DB) and clicked "Sync database schema now" button in Metabase:
2023-06-20 16:38:08 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET extra_float_digits = 3
2023-06-20 16:38:08 UTC:x.xx.xxx.xxx(41164):postgres@postgres:[657]:LOG: execute <unnamed>: SET extra_float_digits = 3
2023-06-20 16:38:08 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET application_name = 'Metabase v0.46.5 [ec32db87-958e-4dfa-8246-38be7319b765]'
2023-06-20 16:38:08 UTC:x.xx.xxx.xxx(41164):postgres@postgres:[657]:LOG: execute <unnamed>: SET application_name = 'Metabase v0.46.5 [ec32db87-958e-4dfa-8246-38be7319b765]'
2023-06-20 16:38:08 UTC:x.xx.xxx.xxx(41164):postgres@postgres:[657]:LOG: execute <unnamed>: SHOW TRANSACTION ISOLATION LEVEL
2023-06-20 16:38:08 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SHOW TRANSACTION ISOLATION LEVEL
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:WARNING: unrecognized node type: 380
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET SESSION CHARACTERISTICS AS TRANSACTION ISOLATION LEVEL READ UNCOMMITTED
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SELECT nspname AS TABLE_SCHEM, NULL AS TABLE_CATALOG FROM pg_catalog.pg_namespace WHERE nspname <> 'pg_toast' AND (nspname !~ '^pg_temp_' OR nspname = (pg_catalog.current_schemas(true))[1]) AND (nspname !~ '^pg_toast_temp_' OR nspname = replace((pg_catalog.current_schemas(true))[1], 'pg_temp_', 'pg_toast_temp_')) ORDER BY TABLE_SCHEM
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SELECT NULL AS TABLE_CAT, n.nspname AS TABLE_SCHEM, c.relname AS TABLE_NAME, CASE n.nspname ~ '^pg_' OR n.nspname = 'information_schema' WHEN true THEN CASE WHEN n.nspname = 'pg_catalog' OR n.nspname = 'information_schema' THEN CASE c.relkind WHEN 'r' THEN 'SYSTEM TABLE' WHEN 'v' THEN 'SYSTEM VIEW' WHEN 'i' THEN 'SYSTEM INDEX' ELSE NULL END WHEN n.nspname = 'pg_toast' THEN CASE c.relkind WHEN 'r' THEN 'SYSTEM TOAST TABLE' WHEN 'i' THEN 'SYSTEM TOAST INDEX' ELSE NULL END ELSE CASE c.relkind WHEN 'r' THEN 'TEMPORARY TABLE' WHEN 'p' THEN 'TEMPORARY TABLE' WHEN 'i' THEN 'TEMPORARY INDEX' WHEN 'S' THEN 'TEMPORARY SEQUENCE' WHEN 'v' THEN 'TEMPORARY VIEW' ELSE NULL END END WHEN false THEN CASE c.relkind WHEN 'r' THEN 'TABLE' WHEN 'p' THEN 'PARTITIONED TABLE' WHEN 'i' THEN 'INDEX' WHEN 'P' then 'PARTITIONED INDEX' WHEN 'S' THEN 'SEQUENCE' WHEN 'v' THEN 'VIEW' WHEN 'c' THEN 'TYPE' WHEN 'f' THEN 'FOREIGN TABLE' WHEN 'm' THEN 'MATERIALIZED VIEW' ELSE NULL END ELSE NULL END AS TABLE_TYPE, d.description AS REMARKS, '' as TYPE_CAT, '' as TYPE_SCHEM, '' as TYPE_NAME, '' AS SELF_REFERENCING_COL_NAME, '' AS REF_GENERATION FROM pg_catalog.pg_namespace n, pg_catalog.pg_class c LEFT JOIN pg_catalog.pg_description d ON (c.oid = d.objoid AND d.objsubid = 0 and d.classoid = 'pg_class'::regclass) WHERE c.relnamespace = n.oid AND n.nspname LIKE 'information_schema' AND c.relname LIKE '%' AND (false OR ( c.relkind = 'r' AND n.nspname !~ '^pg_' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'p' AND n.nspname !~ '^pg_' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'v' AND n.nspname <> 'pg_catalog' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'f' ) OR ( c.relkind = 'm' ) ) ORDER BY TABLE_TYPE,TABLE_SCHEM,TABLE_NAME
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SELECT NULL AS TABLE_CAT, n.nspname AS TABLE_SCHEM, c.relname AS TABLE_NAME, CASE n.nspname ~ '^pg_' OR n.nspname = 'information_schema' WHEN true THEN CASE WHEN n.nspname = 'pg_catalog' OR n.nspname = 'information_schema' THEN CASE c.relkind WHEN 'r' THEN 'SYSTEM TABLE' WHEN 'v' THEN 'SYSTEM VIEW' WHEN 'i' THEN 'SYSTEM INDEX' ELSE NULL END WHEN n.nspname = 'pg_toast' THEN CASE c.relkind WHEN 'r' THEN 'SYSTEM TOAST TABLE' WHEN 'i' THEN 'SYSTEM TOAST INDEX' ELSE NULL END ELSE CASE c.relkind WHEN 'r' THEN 'TEMPORARY TABLE' WHEN 'p' THEN 'TEMPORARY TABLE' WHEN 'i' THEN 'TEMPORARY INDEX' WHEN 'S' THEN 'TEMPORARY SEQUENCE' WHEN 'v' THEN 'TEMPORARY VIEW' ELSE NULL END END WHEN false THEN CASE c.relkind WHEN 'r' THEN 'TABLE' WHEN 'p' THEN 'PARTITIONED TABLE' WHEN 'i' THEN 'INDEX' WHEN 'P' then 'PARTITIONED INDEX' WHEN 'S' THEN 'SEQUENCE' WHEN 'v' THEN 'VIEW' WHEN 'c' THEN 'TYPE' WHEN 'f' THEN 'FOREIGN TABLE' WHEN 'm' THEN 'MATERIALIZED VIEW' ELSE NULL END ELSE NULL END AS TABLE_TYPE, d.description AS REMARKS, '' as TYPE_CAT, '' as TYPE_SCHEM, '' as TYPE_NAME, '' AS SELF_REFERENCING_COL_NAME, '' AS REF_GENERATION FROM pg_catalog.pg_namespace n, pg_catalog.pg_class c LEFT JOIN pg_catalog.pg_description d ON (c.oid = d.objoid AND d.objsubid = 0 and d.classoid = 'pg_class'::regclass) WHERE c.relnamespace = n.oid AND n.nspname LIKE 'pg_catalog' AND c.relname LIKE '%' AND (false OR ( c.relkind = 'r' AND n.nspname !~ '^pg_' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'p' AND n.nspname !~ '^pg_' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'v' AND n.nspname <> 'pg_catalog' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'f' ) OR ( c.relkind = 'm' ) ) ORDER BY TABLE_TYPE,TABLE_SCHEM,TABLE_NAME
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SELECT NULL AS TABLE_CAT, n.nspname AS TABLE_SCHEM, c.relname AS TABLE_NAME, CASE n.nspname ~ '^pg_' OR n.nspname = 'information_schema' WHEN true THEN CASE WHEN n.nspname = 'pg_catalog' OR n.nspname = 'information_schema' THEN CASE c.relkind WHEN 'r' THEN 'SYSTEM TABLE' WHEN 'v' THEN 'SYSTEM VIEW' WHEN 'i' THEN 'SYSTEM INDEX' ELSE NULL END WHEN n.nspname = 'pg_toast' THEN CASE c.relkind WHEN 'r' THEN 'SYSTEM TOAST TABLE' WHEN 'i' THEN 'SYSTEM TOAST INDEX' ELSE NULL END ELSE CASE c.relkind WHEN 'r' THEN 'TEMPORARY TABLE' WHEN 'p' THEN 'TEMPORARY TABLE' WHEN 'i' THEN 'TEMPORARY INDEX' WHEN 'S' THEN 'TEMPORARY SEQUENCE' WHEN 'v' THEN 'TEMPORARY VIEW' ELSE NULL END END WHEN false THEN CASE c.relkind WHEN 'r' THEN 'TABLE' WHEN 'p' THEN 'PARTITIONED TABLE' WHEN 'i' THEN 'INDEX' WHEN 'P' then 'PARTITIONED INDEX' WHEN 'S' THEN 'SEQUENCE' WHEN 'v' THEN 'VIEW' WHEN 'c' THEN 'TYPE' WHEN 'f' THEN 'FOREIGN TABLE' WHEN 'm' THEN 'MATERIALIZED VIEW' ELSE NULL END ELSE NULL END AS TABLE_TYPE, d.description AS REMARKS, '' as TYPE_CAT, '' as TYPE_SCHEM, '' as TYPE_NAME, '' AS SELF_REFERENCING_COL_NAME, '' AS REF_GENERATION FROM pg_catalog.pg_namespace n, pg_catalog.pg_class c LEFT JOIN pg_catalog.pg_description d ON (c.oid = d.objoid AND d.objsubid = 0 and d.classoid = 'pg_class'::regclass) WHERE c.relnamespace = n.oid AND n.nspname LIKE 'public' AND c.relname LIKE '%' AND (false OR ( c.relkind = 'r' AND n.nspname !~ '^pg_' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'p' AND n.nspname !~ '^pg_' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'v' AND n.nspname <> 'pg_catalog' AND n.nspname <> 'information_schema' ) OR ( c.relkind = 'f' ) OR ( c.relkind = 'm' ) ) ORDER BY TABLE_TYPE,TABLE_SCHEM,TABLE_NAME
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:WARNING: unrecognized node type: 380
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET SESSION CHARACTERISTICS AS TRANSACTION ISOLATION LEVEL READ COMMITTED
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:WARNING: unrecognized node type: 380
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET SESSION CHARACTERISTICS AS TRANSACTION ISOLATION LEVEL READ UNCOMMITTED
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET SESSION TIMEZONE TO 'UTC'
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: BEGIN READ ONLY
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>/C_1: -- Metabase
select to_char(current_timestamp, 'YYYY-MM-DD HH24:MI:SS.MS TZ')
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute S_2: ROLLBACK
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:WARNING: unrecognized node type: 380
2023-06-20 16:38:09 UTC:x.xx.xxx.xxx(41162):postgres@postgres:[656]:LOG: execute <unnamed>: SET SESSION CHARACTERISTICS AS TRANSACTION ISOLATION LEVEL READ COMMITTED
This happens on Aurora Provisioned Postgres 15.2 and ServerlessV2.