Jest, TypeScript and ts-jest: SyntaxError: Cannot use import statement outside a module

Question

I'm working on testing an Apollo Server using Jest and SuperTest. The server is written in TypeScript, so I'm using ts-jest. I need to bind SuperTest to a particular port. The SuperTest docs say

You may pass an http.Server, or a Function to request() - if the server is not already listening for connections then it is bound to an ephemeral port for you so there is no need to keep track of ports.

so I want to pass in my app. I've set up my index file to export the Apollo Server

// index.ts
import { ApolloServer } from 'apollo-server';
...
const start = () => {
    ...
    const server = new ApolloServer(config);
    server.listen().then(({ url }) => {
        log.info(`interface server 📡 Running at ${url}`);
    });
    return server;
};

const app = start();

export default app;

However when I run my code

// __test__/index.ts
import { default as request } from 'supertest';
import log from '../util/log';
import app from '../index';

let postData = {
    query: `query allArticles {
                allArticles {
                    id
                }
            }`,
    operationName: 'allArticles'
};

test('basic', async () => {
    try {
        const response = await request(app)
            .post('/graphql')
            .send(postData)
            .expect(200); // status code that you expect to be returned
        log.info('response', response.statusCode);
    } catch (error) {
        log.info(`error ${error.toString()}`);
    }
});

I get

 FAIL  __test__/index.test.ts
  ● Test suite failed to run

    Details:

    /Users/abc/Documents/projects/yaa-interface-new/index.js:1
    import { ApolloServer } from "apollo-server";
    ^^^^^^

    SyntaxError: Cannot use import statement outside a module

      1 | import { default as request } from 'supertest';
      2 | import log from '../util/log';
    > 3 | import app from '../index';
        | ^

For some reason jest is looking in /index.js instead of index.ts ? (The js files should all be going into /dist-- see tsconfig below). According to this Stack Overflow question, I need to add Babel to Jest. I've tried to set up both ts-jest and Jest to use Babel but I confess I am unclear what I'm doing. In any case, I get the same error. Any clues much appreciated!

My jest.config.js:

 // jest.config.js
module.exports = {
    preset: 'ts-jest/presets/js-with-babel',
    testEnvironment: 'node',
    globals: {
        'ts-jest': {
            babelConfig: true
        }
    }
};

and my tsconfig.json:

 // tsconfig.json
{
  "compilerOptions": {
    "target": "ES6",
    "lib": [
      "esnext",
      "dom"
    ],
    "skipLibCheck": true,
    "outDir": "dist",
    "strict": false,
    "forceConsistentCasingInFileNames": true,
    "esModuleInterop": true,
    "module": "commonjs",
    "moduleResolution": "node",
    "resolveJsonModule": true,
    "isolatedModules": true,
    "sourceMap": true,
    "alwaysStrict": true
  },
  "exclude": [
    "node_modules",
    "**/*.test.ts",
    "**/*.mock.ts"
  ]
}