I will suggest trying Beeceptor, that helps to build mock API in no time. Easy to use for most businesses or developers who are struggling with API.

https://beeceptor.com/mock-server/fake-store-api

Basically it is very important to start with a correct setup to avoid struggling with unexpected use cases later that may result in refactoring of a lot of code. In case you start with a frontend that is based on an api without having an api, I recommend to you to avoid mocking a backend fake API yourself but use a already existing solution.

A very useful tool which i can hightly recommend for mocking a fake backend API, especially for beginners, is jsonserver.io.

For later API url switch, I recommend to use .env for defining the API urls. The use of .env files requires the dotenv lib you can get from here. The use of dotenv allows you to define different .env files like a .env.development or .env.production or whatever you like. For loading the correct env you have just to do the following:

require('dotenv').config({ path: `.env.${process.env.NODE_ENV}` })

This would load the .env based on the NODE_ENV (development/production). The .env files can contain the vars which define the URLs you need for your backend like BASE_API_URL. If you decide to use e.g jsonserver.io, the development env would define

BASE_API_URL=https://api.jsonserver.io

and the production (or whatever you're going to name it for further non-production urls)

BASE_API_URL=https://your-domain.com

Finally you have to set base url in your axios configuration section at nuxt.config.js

axios: {
    browserBaseURL: process.env.BASE_API_URL,
    ....
}

Thats it, just adapt you NODE_ENV or your custom indicator which you want to use for the condition to load the right env file.

NOTE: If you use axios proxy, you have to define the API urls from env in your proxy configuration and use the base browser url as axios base url.