How to correctly set axios.baseUrl in Nuxt, what would work on both local and domain?

Question

Vue.js

Good afternoon! Initially it was like this:

axios: {
    baseURL: process.env.NODE_ENV === 'production'
      ? 'https://site-name.ru'
      : 'http://localhost:3000'
 },

My joy knew no bounds until I accidentally went to www .site-name.ru and discovered that requests go to a domain without www and are blocked by CORS policy => the domain with www becomes inoperable.
Next I tried:

axios: {
    baseURL: '/'
 },

But even here the moment - the code from nuxtServerInit stops working correctly.
nuxtServerInit:

async nuxtServerInit({ dispatch, getters, commit }) {
    const isUserSigned = await dispatch('auth/autoSignin');

    if (isUserSigned) await dispatch('auth/getUserByToken');
}

store/auth

async getUserByToken({commit, dispatch}) {
    try {
      const user = await this.$axios.$get('/api/auth/getUserByToken');

      if (user && user.id) {
        dispatch('setUser', user);
      } else {
        dispatch('signout', false);
      }

    } catch (e) {
      console.log(e.message);
      dispatch('setUser', null);
      dispatch('signout', false);
    }
},

That is, the response from the server is 404 because the request is sent to http:/api/auth/getUserByToken' (literally).
With the rest of the requests, everything is in order, in any case, so far the problem is relevant only for nuxtServerInit.
What do you advise?