weather-cli | Check the weather for your city from your terminal | Command Line Interface library

You can't change the route or use the Vue-router from inside the Electron main process, as you also can't access the Electron Menu from inside any Vue component for activating / deactivate submenus according to the login state (another doubt I had posted and answered myself).

Electron Menus should always be managed at the Electron main process.

Vue routes should always be managed at the Electron renderer process - from inside Vue components.

So, as the events are generated on layers different from the ones where they should be treated, in both cases, just notify each other layer, through IPC messages, that you want that thing to change and it will be changed there, at the proper layer.

In the case of changing the Menu, the login / logout Vuex state is checked inside the Vue components, then the component sends an IPC call to the main process and the submenus are activated or deactivated there. See this solution on the link:
How to activate / deactivate an Electron.js submenu from inside a Vue.js Component according to a specific Vuex state?

Another similar solution is the one for this post problem, but the other way around:

For changing the routes, instead of using win.loadURL() or win.loadFile() at the main process side, one should send an IPC call to the renderer side, in this case to the App.vue component, using win!.webContents.send("changeRouteTo", "/"), for example. The "changeRouteTo" is a custom channel name and the "/" is the path to which the router, from inside the Vue component, at the renderer side, will change the route to - for the "/" it's the "Home" route. For changing to the "Login" route, the path would be "/login", and so on... according to the router.ts config. At the renderer side, in this case at the App.vue component, it is set an IPC renderer listener for the "changeRouteTo" channel or event, and, each time it receives a route change request from the main process, then this.$router.push() is used, from inside this component, to change the route to that correspondent route.

This should work both for development and non development environments, when using npm run electron:serve to run the project, as for the final build execution, after npm run electron:build is called and a bundle is created.

Hope this solution is useful to others.

See the full final project here, it's a pretty nice sample app:
https://github.com/danielpm1982/open-weather-client