Is it possible to use Framework7 (with Vue) to create essentially a mobile website running on a server without packaging it as a native web-view app?
Sure, like all the Kitchen Sink and live examples work, e.g. https://framework7io.github.io/framework7-template-vue-simple/
But I can’t open the index.hml locally without running
npm run serve?
You can, if you open file directly (via file:// protocol) you may need to tweak scripts and styles paths not to have “/“ in the beginning. Just use relative paths. And your question was about running on the server