In the 'not exists' cluster, you do not have to search table "Vacancy as v"
again.
I think it would be faster to use the outer Vacancy table as below.
In your case, that do the same work.
NOT EXISTS (
SELECT 1
FROM "CategoryOption_TableRow" "ct126"
WHERE "Vacancy"."Template"
AND "ct126"."CategoryOptionID" IN (34024,35254,35255,35256)
AND "ct126"."Category_TableID" = 126
AND "ct126"."RowID" = "Vacancy"."ID"
)