This is how I like to run Sanity Studio. Alongside .env file I have env.js file that looks like this:

export const studioApiVersion = process.env.SANITY_STUDIO_API_VERSION
export const studioProjectID = process.env.SANITY_STUDIO_PROJECT_ID
export const studioDataset = process.env.SANITY_STUDIO_DATASET
...

When I want to use an env variable I import it:

import { studioProjectID, studioDataset } from './env'

It works locally, deployed on the Sanity Studio domain, and on Cloudflare Pages, which I like to use.