Elasticsearch: how to execute a query using quoted partial phrases

I am trying to implement a search behavior that supports partial phrases. A possible search entry might look like this:

example "hello world" elasticsearch

Now I want to get all documents containing words example

and elasticsearch

as well as the phrase hello world

.

Since this is a very typical use case for searches, I was surprised that I couldn't find much on this topic.

I tried several approaches (templated tokenizer, picture grab filter), but none of them worked as expected. Before I start implementing a dedicated approach for creating a complex query definition programmatically, is there a recommended way to achieve this?

Any help is greatly appreciated!