This is the default popup style in the 4x versions of the JS API. By "standard popup" do you mean the popup in the class map viewer (3x JS API)?
If you want to take advantage of this in webmaps you can use it in any JS API 4x app, or in the map viewer beta.
I am using version 4.18 but my popup does not look like the picture I posted in the example. Mainly what I am looking for is to have a single large popup action button on the bottom of my popup like in the sceneview popup picture I posted where the 'zoom to' action is a large green button. My popup has small action icons I have attached a screenshot. What am I doing wrong?
there is no out of the box style similar with the SceneViewer one, you'll have to do all the styling yourself.
Here is some basic css that the sceneviewer also uses, to get you started: https://codepen.io/ralucanicola/pen/poRMagR?editors=1000