Enable arcgis API JS popups with Vue CLI 3

Your code is fine, you are just not adding css. You are missing { css: true }, that’s all.

loadModules(
  ["esri/Map", "esri/views/MapView", "esri/layers/FeatureLayer"],
  { css: true } // <-- HERE
).then(([ArcGISMap, MapView, FeatureLayer]) => {
  //...
}

HERE code with the fix.