I don't know why exactly you need BigQuery in your scenario. If I wanted to have Postgres->ClickHouse it would take single INSERT SELECT from ClickHouse.

If you need just CSV result dumped to GCS you can use clickhouse-local mode that has all the features like integrations with Postgres, GCP, formats.

Only but it is not a service with UI where your data analysts can click and drag what they want to export. But SQL can be simple for them to write and you need nothing more than a trivial cron job analogue to run it.