Is PgAudit extension database specific?

Here is my observation:

Connected to postgres DB and ran:

CREATE EXTENSION pgaudit;

Within postgres DB, I ran this:

SELECT * FROM pg_catalog.pg_extension WHERE extname = 'pgaudit';

It does return a row.

I changed the DB and ran the same SQL, but it does not return any thing.

The PostgreSQL instance is a GCP cloud SQL running with postgres V14.19.

Would you help me understand this, please.

Regards

Siraj