Transfer a column into a new Table, also adding a mapping Table in between

I was lazy when I originally created a table where one column could contain multiple email addresses, separated by commas, spaces or returns in the field.

Now I like to create a separate table that holds just the email addresses. This can lead to multiple emails belonging to the same original row, so I also like to have a mapping table that links the one or more email rows to the original rows (I understand that for this 1-to-many case where each email can only belong to one customer, this extra map table is not required, but for the sake of solving the specific challenge behind it I like to keep this map relevant for this question).

There are two challenges for me:

1. How to I write the SELECT so that I get multiple rows for the comma separated values? The solution I found is to use UNNEST(string_to_array(regexp_replace(TRIM(emails),'\s+',',','g'),',')). (The TRIM is for safety, removing extra spaces around the field, so that I do not end up with empty rows - is there a better way, e.g. by removing empty elems from the array? Searching locates this, which seems to be needlessly complex for my case, though)
2. When I create the mapping row, I need two ids. How do I get these two values? One I get from inserting new rows based on the original rows, but I also need the original row's id. Which means that when I select the original rows, I need to fetch its id along with the emails - but I do not understand how to keep it around while using the emails for the insertion.

Example

Original data

DROP TABLE IF EXISTS test_customers;CREATE TABLE test_customers (id SERIAL PRIMARY KEY, emails TEXT);INSERT INTO test_customers (emails) VALUES ('a@x.com'), ('b1@x.com,b2@x.com');SELECT * FROM test_customers;

Table test_customers

Desired outcome

The new tables

DROP TABLE IF EXISTS test_emails;CREATE TABLE test_emails (  id SERIAL PRIMARY KEY,  email TEXT);DROP TABLE IF EXISTS test_map;CREATE TABLE test_map (  cust_id SERIAL,  email_id SERIAL,  CONSTRAINT fk_customer FOREIGN KEY(cust_id) REFERENCES test_customers(id),  CONSTRAINT fk_email FOREIGN KEY(email_id) REFERENCES test_emails(id));

Table test_customers

Basically, the email column isn't needed any more (I can simply drop that in the end, a no brainer):

Table test_emails

The emails are now here:

Table test_map

And this links the emails to the customers:

My SQL code for converting all rows, so far

WITH map_ins AS (  INSERT INTO test_emails (email)  SELECT    id AS cust_id,    UNNEST(string_to_array(regexp_replace(TRIM(emails),'\s+',',','g'),','))    FROM test_customers  RETURNING id AS email_id, cust_id)INSERT INTO test_map (cust_id, email_id) VALUES (cust_id, email_id);

This gives an error:

INSERT has more expressions than target columns

That's where I'm stuck. The first SELECT needs to fetch both the id and the emails so that I can return them further down, but if I do that, then how do I omit it in the INSERT where I only want to insert the email but not the id into the row?