We resolvede server side on development using a proxy bypass with origin rewrite. For production server we’re unable to enable origin ‘*’ so we’ll try to add a reverse proxy or a pass through proxy like done in development.
VueJS cannot use MongoDB directly. VueJS is a frontend library (works in the browser), while MongoDB is a server-side database technology. In the course you mentioned, the author is probably bridging VueJS and MongoDB through an ExpressJS app, which runs in a server. You should be seeing things like fetch( or axios in the examples. Those words indicate the client-side application connecting to a backend.
The models are probably written for a MongoDB library that runs in ExpressJS. Controllers must be either self-developed or using a library that allows creating controllers for ExpressJS.
Notice I keep saying ExpressJS. There are other server frameworks for NodeJS, but ExpressJS is the most popular one.