Yes, the FDWs developed by Wrappers can be used on any Postgres db.
| Do I have to run Supabase to take advantage of the FDWs created through this framework?
No, you don't need to. Those are just normal FDWs can be used on any Postgres db.
| Is there a generic JDBC/SQL/etc FDW for any SQL based database like Snowflake, Oracle, etc?
The Snowflake FDW isn't developed yet, the example is just for concept demo. It has ClickHouse and BigQuery FDWs although they are not JDBC based. Generic JDBC FDW will need JVM embedded so it is not in plan at this moment.
Disclaimer: I am Supabase developer.