How do I exclude a node from an entity reference field?
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You are right, you can do that with the help of a Relationship and a Contextual filter, but details are important. 

In your Latest articles Views add the Relationship named something like Content referenced from field_myERfield for your featured article field. Be careful about the wording there because there are two Relationships available for the same field, you want the "backwards" one. Don't require the Relationship, otherwise you'll get no results if your home page isn't an article type. 

Add the Contextual ID filter and set it to use the Relationship you've just added. Provide default value and choose Content ID from URL. Under Validation choose Content and Article, and other options that make sense in your case. 

Then under More choose Exclude. That is how you exclude the currently featured article(s) from the latest articles list. 

If you don't choose Exclude you'll only see the featured article in the results.