The general rule of thumb of using await findBy query and await waitFor is that you should use

await findBy when you expect an element to appear but the change to the DOM might not happen immediately.

and await waitFor when you have a unit test that mocks API calls and you need to wait for your mock promises to resolve.

The same is mentioned in the official documentation of the dom-testing-library.

Now coming to your concern, you need to use jest.useFakeTimer() to enable fake timers that will help in mocking the setTimeout and other timer functions.

The same is mentioned here in official docs.

useFakeTimer works with the async methods, however, if we want to work with sync methods like getBy queries then we have to use jest.advanceTimersByTime(5000) to move your test 5 (any specified time) seconds ahead of it. (example given below)

In the following example, I reproduce the concern that you have raised. I think this might help.

import { useState } from 'react';
import { act, render, screen, waitForElementToBeRemoved } from '@testing-library/react';
import userEvent from '@testing-library/user-event';

const data = {
  name: 'subrato',
  age: 24,
};


function App() {
  const [myData, setState] = useState({});
  const [loading, setLoading] = useState(false);

  function clickHandler() {
    setLoading(true);
    setTimeout(() => {
      setState(data);
      setLoading(false);
    }, 5000);
  }

  return (
    <div className='App'>
      {loading && <div aria-label='loading'>loading....</div>}
      <p>{myData?.name}</p>
      <p>{myData?.age}</p>
      <button onClick={clickHandler}>Click me</button>
    </div>
  );
}
describe('Test my app', () => {
  beforeEach(() => {
    jest.useFakeTimers();
  });

  afterEach(() => {
    jest.useRealTimers();
  });

  it('display data', async () => {
    render(<App />);

    userEvent.click(screen.getByText('Click me'));

    expect(screen.getByLabelText(/loading/i)).toBeInTheDocument();

    expect(await screen.findByText('subrato')).toBeInTheDocument();
    expect(screen.getByText('24')).toBeInTheDocument();
   
  });

  it('display data second time', async () => {
    render(<App />);

    userEvent.click(screen.getByText('Click me'));

    expect(screen.getByLabelText(/loading/i)).toBeInTheDocument();

    act(() => jest.advanceTimersByTime(5000));

    expect(screen.getByText('subrato')).toBeInTheDocument();
    expect(screen.getByText('24')).toBeInTheDocument();
   
  });
});

Test Result

 PASS  src/TimerExample.spec.tsx (9.001 s)
  Test my app
    √ display data (487 ms)
    √ display data second time (35 ms)

Test Suites: 1 passed, 1 total
Tests:       2 passed, 2 total
Snapshots:   0 total
Time:        14.997 s
Ran all test suites matching /TimerExample.spec.tsx/i.