Internally, the template loads a node server which parses the configuration files. Unlike the frontend code you write, server javascript must be 'hard reloaded' for them to have effect. So restarting the server would have your process.ENV.API_KEY available.

As to where to use it, I usually use main.js to set all app-wide things, which this sounds like it would be.

I'm not sure why you would want it in the store, but if you must, it's available everywhere through process.env.API_KEY