How to index only some of the fields of the entire document?

ESS and APP Search are related but not the same thing ...

ESS is the Elasticsearch Service which includes Elasticsearch and Elasticsearch App Search which is a Solution that "Sits On Top Of" Elasticsearch.

App Search is built to simplify the App Search experience and so not every feature of the underlying Elasticsearch is supported.

I do not think the same feature is available in App Search.

If you wanted to not index fields you will need to remove them from the incoming / source JSON

(I am double checking this, but pretty sure)