Testing an error thrown by a React component using testing-library and jest

As you already mentioned there is expect().toThrow() 🙂

So in your case:

  test("should throw error when not wrapped inside `UserProvider`", () => {
    expect(() => render(<TestComponent />))
      .toThrow("Cannot use `useUser` outside of `UserProvider`");
  });

Regarding the console.error:
Currently there is by design no way to turn off the default error logs.
If you want to hide errors, you still need to mock console.error.

When you mock functions like console.error you want to restore them in a afterEach callback so that they are also restored if the test fails.