I struggled on the same issue and “mysql syntax is non-standard” is not a valid argument in my opinion. PostgreSQL adds handy non-standard extensions as well, for example “INSERT … RETURNING …” to get auto ids after inserts. Also, repeating large queries is not an elegant solution.
However, I found the WITH statement very helpful (CTE’s). It sort of creates a temporary view within the query which you can use like a usual table then. I’m not sure if I have rewritten your JOIN correctly, but in general it should work like this:
WITH jobs_refined AS (
SELECT
jobs.*,
(SELECT CASE WHEN lead_informations.state IS NOT NULL THEN lead_informations.state ELSE 'NEW' END) AS lead_state
FROM jobs
LEFT JOIN lead_informations
ON lead_informations.job_id = jobs.id
AND lead_informations.mechanic_id = 3
)
SELECT *
FROM jobs_refined
WHERE lead_state="NEW"