I’ve read the docs:
https://codesandbox.io/docs/learn/environment/secrets

And I have stored my environment variables accordingly:

However, when I actually try to access these environment variables in the code with:

const GOOGLE_MAPS_API_KEY = process.env.GOOGLE_MAPS_API_KEY;

…it doesn’t work. And yes I have already confirmed that my API request works properly if I hard-code the API KEYs.

Is process.env.[VAR_NAME] not the correct way to do this?

AFAIK, this is the standard way that environment variables are accessed in a React project. Unfortunately, there is nothing in the CodeSandbox docs that specifies how to access the environment variables. They only tell you where to store them.