Thank you for the credentials. I have temporarily switched the theme to a standard one (“Twenty Fifteen”) and tried adding a featured image. That actually did not work. So this is not a Narrator-related issue, as it also happens with standard themes in your particular environment.
Then I deactivated the plugins (except the ones recommended by Narrator). And the featured image functionality started working — you can see I’ve added a test image.
So one of your plugins seems to be breaking it. You can try re-enabling them one-by-one to see which plugin it is.