[Vuejs]-Node.js/Express: Pass routes/ let other routes than root handle by the Single page application

Like you already said in your explanation, you have a SPA and the routing is being handled by Vue in the frontend. Retuning your index.html for every route and letting Vue do its thing in the frontend is the way to go.

And secondly, is that the recommended / or even standard way how to pass that route handling to your SPA and not by node.js? Or is there another better way?

The other options would be to have a server site app, meaning building the page on everything request. What Next.js does in React.

Or to have static pages, like what Gatsby does in React.