Row level security with a single DB user and connection pooling
I have a similar setup on a new project.

The issue here is that you have a connection pool that uses a single login. The application that holds that connection pool will need to set the user correctly to get the required row level permissions. If your application is incorrectly configured / coded, then the permissions can be subverted.

It seems to me that row level permissions are only really useful when you have different users/roles with different logins reading from tables directly. In that case there is no where user = xxxx style clause that can be subverted. In this situation they make different connections.