Postgresql and jsonb: perform a like over all values of an array
You can use the following query

SELECT 
    id_user 
FROM
    users
    JOIN LATERAL jsonb_array_elements(emails) AS x(email) ON true
WHERE
    email::text like '%email%' ;


jsonb_array_elements() returns a SET OF jsonb objects. You join them to user_id using a JOIN LATERAL. Then use a WHERE clause where you convert these jsonb objects to text, and then use your like '%email%'.

You can check a simple setup at dbfiddle.

NOTE: If you do not want repeated values: GROUP BY.