pgAudit not logging anything in GCP Cloud SQL - postgresql

Question

I'm hoping for some insight into a problem I'm having with using pgAudit for a PostgreSQL 12 managed instance in GCP Cloud SQL.
Thus far, I've done the following to set this up:
Database flags:
cloudsql.enable_pgaudit=on
pgaudit.log=ddl
pgaudit.log_client=yes (turned this one on for debugging purposes)
pgaudit.log_relation=on
After enabled the cloudsql.enable_pgaudit flag and restarting the instance, I issued a CREATE EXTENSION pgaudit command, and confirmed that it was successful. I've also enabled the data access logs as suggested in the Google documentation (they didn't specify which permissions were needed in IAM, so I erred on the side of everything). I've also tried setting pgaudit.log=all to see if ANYTHING could be captured, with the same catch that nothing is being logged.
With pgaudit.log_client=on, I would expect to see the audit log information returned when viewing the Server Output in DBeaver, but nothing appears there.
Anyone have any insight as to what I might be missing? My goal, ultimately is to capture DDL operations with session logging. I've generally attempted testing by creating a dropping a table in an effort to get the log for those operations, i.e.
create table dstest_table (columnone varchar(150));
drop table dstest_table;
I've tried a few more things to get this to work, including setting the flags additionally at the database level. So far, nothing seems to be getting logged.
Update: Never did get pgAudit to work properly, however, found that DDL operations can be logged outside of pgAudit via the log_statement=ddl flag on the server. Set this, and I'm now getting what I need.
Database Flags
Cloud Logging API Data Access Log
Cloud SQL Data Access Log

Answer 1

log_statement=ddl as a flag allows for logging DDL statements without using pgAudit, so the majority of the setup was unnecessary. Set this flag and the operations I needed are now logged.