Postgres: empty table though permissions granted to the role

I have a problem with SELECT when granting permission for the role.

I need to create a Customer role with the privilege to SELECT from 2 tables. And then I need to create a personalized role for one client, and GRANT customer to this role.

I did it this way:

CREATE ROLE customer;

GRANT SELECT ON public.payment TO customer;
GRANT SELECT ON public.customer TO customer;

ALTER TABLE public.payment ENABLE ROW LEVEL SECURITY;

CREATE POLICY policy_payments
ON public.payment TO customer
USING (customer_id = (
            SELECT customer_id
            FROM public.customer c
            WHERE 'client_' || lower(c.first_name || '_' || c.last_name) = current_role));
    
CREATE role client_julie_sanchez;

GRANT customer TO client_julie_sanchez;
  
SET ROLE client_julie_sanchez;
SELECT * FROM public.payment p

I see an empty table for both roles - Customer and client_julie_sanchez. What's wrong with the code?