VueJS SPA for WP admin menu page not working
I've gotten similar Vue.js widgets to work with WP, but only using browserify, instead of webpack.
I didn't use the browserify template of vue-cli, although it could work with that. Instead I used my own package.json. Here's the gist: https://gist.github.com/maurop123/eb0c8e884fefe3e40c110b33beff48db
That will make a single file dist/bundle.js for the whole vue app. I then dropped that file into wherever the static js files are for my wp theme.
Next, I added a wp_enqueue_script line in functions.php like this...
wp_enqueue_script( MD_THEME_NAME.'-bundle', MD_THEME_URI.'/assets/js/bundle.js', array('jquery'), NULL, true );
The particular pattern of arguments may depend on your theme. You should try to make your wp_enqueue_script look like existing one.
Finally, I added the html element needed ,like <div id="vueApp"></div> for example, anywhere in the currently rendered template.
Hope that helps!