You have a couple of choices.
Also, a slight aside, if you aren't comfortable with using VueJS as a framework, you are free to use an alternative such as jQuery, REACT, Angular, etc. Or indeed to roll your own.
So, the choices:
- Interact with your API direct from the front end. In other words, use your front-end code to call the REST API directly.
- Interact with the API from Node-RED. Sending the user input back to node-red (see the button code in the default template) and using the resulting msg output from the uibuilder node to send into an http-request node, get the result, process it if needed and send it back to the front-end by passing it to the input of the uibuilder node.
Which you chose is up to you. I'd guess that 1. may be more efficient but harder to code.