Query about pg_wal directory filled up

One of our clients recently migrated from Oracle to PostgreSQL and is conducting multiple scenarios to understand PostgreSQL behavior.  

One of their main concerns is whether the database will allow `INSERT` queries when the `pg_wal` directory becomes full.  

As I understand, once the `pg_wal` directory is completely filled, the database will allow only read queries and will not permit any write operations.  

Kindly advise

Thanks

RK