LISTEN / NOTIFY privileges
There are no permissions on LISTEN and NOTIFY. It would not have made sense to have any until support for notify payloads was introduced in more recent versions.

If you want access control, create a table with the information that you want and then send a NOTIFY that's empty or has nothing but a primary key for that table in it. SELECT the row(s) of interest from the table, which can have access control, to get the sensitive data. This used to be the only way to use LISTEN and NOTIFY to send specific data before payloads were added.