Your logstash output has a conditional against the field [fields][product], but you do not have this field in your document, so this conditional will always be false.
You have fields_under_root set to true in your filebeat.yml, so every field you add will be in the root of your document, you won't have [fields][product] you will have [product].
You need to change your conditional to use [product] instead of [fields][product] or you can change your filebeat.yml and set fields_under_root to false.