Next.js 12, Jest & Testing Library (Rust compiler setup) error: "Support for the experimental syntax 'jsx' isn't currently enabled"

I am setting up Jest & React Testing Library in Next.js 12.1.6, using the new Rust compiler setup, as described here. Jest-only testing is fine, but when I try to render a component in my test file, I get an error:

"Support for the experimental syntax 'jsx' isn't currently enabled (11:12)"

My understanding of how Next.js and/or Babel and Jest all work together under the hood is sketchy at best, but the way I understand it, Babel is bypassed when using the Next.js 12 Rust compiler. I figure that the JSX is supposed to be transformed by Next before it gets to Jest, and I figure that this is not happening. I have no idea what additional configuration I could even attempt in order to fix this. I can't find any hints online, and nobody else seems to be having the same problem. I have read numerous articles and watched a plethora of videos featuring people breezing through the same setup. I have retraced their steps to no avail.

So, I decided to try and set Jest up to use Babel for the transformation, keeping the existing configuration and adding a .babelrc file:

    {
       "presets": ["@babel/preset-env", "@babel/preset-react"]
    }

and then adding the following line to my customJestConfig in jest.config.js (and installing the appropriate modules, of course.

    transform: {"\\.[jt]sx?$": "babel-jest"}

I don't know whether this idea was sensible or comical, but either way it didn't work.

How can I resolve this situation so that I am able to use JSX with Jest & Testing Library using the Rust compiler setup?

    // package.json
    
    {
      "name": "my-app",
      "version": "0.1.0",
      "private": true,
      "scripts": {
        "dev": "next dev",
        "build": "next build",
        "start": "next start",
        "lint": "next lint"
      },
      "dependencies": {
        "next": "12.1.6",
        "react": "17.0.2",
        "react-dom": "17.0.2",
        "react-redux": "^7.2.6",
        "@reduxjs/toolkit": "^1.7.2",
        "next-redux-wrapper": "^7.0.5"
      },
      "devDependencies": {
        "@types/node": "18.0.0",
        "@types/react": "18.0.14",
        "@types/react-dom": "18.0.5",
        "eslint": "8.18.0",
        "eslint-config-next": "12.1.6",
        "typescript": "4.7.4",
        "jest": "28.1.1",
        "@types/jest": "28.1.2",
        "jest-environment-jsdom": "28.1.1",
        "@testing-library/jest-dom": "5.16.4",
        "@testing-library/react": "13.3.0",
        "@testing-library/user-event": "14.2.1"
      }
    }

    // jest.config.js
    
    import nextJest from "next/jest";
    
    const createJestConfig = nextJest({dir: '.'})
    
    const customJestConfig = {
        testEnvironment: "jest-environment-jsdom",
        clearMocks: true,
        moduleDirectories: ["node_modules", "<rootDir>/"],
        setupFilesAfterEnv: ['<rootDir>/jest.setup.js'],
        transform: {"\\.[jt]sx?$": "babel-jest"}
    }
    
    export default createJestConfig(customJestConfig)

    // jest.setup.js
    
    import "@testing-library/jest-dom/extend-expect"

    // example-test.test.tsx
    
    import {render, screen} from "@testing-library/react"
    import userEvent from "@testing-library/user-event";
    
    import Home from "../pages/index"
    
    it("renders Home", function () {
        render(<Home />)
    
        const heading = screen.getByRole('heading', {
            name: /test/i,
        })
    
        expect(heading).toBeInTheDocument()
    })