You should use toBeVisible matcher.

This allows you to check if an element is currently visible to the user. An element is visible if all the following conditions are met:

• it is present in the document
• it does not have its css property display set to none
• it does not have its css property visibility set to either hidden or collapse
• it does not have its css property opacity set to 0
• its parent element is also visible (and so on up to the top of the DOM tree)
• it does not have the hidden attribute
• if <details /> it has the open attribute

E.g.

index.tsx:

import React from 'react';
import { useEffect, useState } from 'react';

const id = 'popup-active';
const Popup = (props) => {
  const [popupActive, setPopupActive] = useState(() => {
    const value = window.localStorage.getItem(id);
    return value !== null ? JSON.parse(value) : true;
  });

  useEffect(() => {
    window.localStorage.setItem(id, popupActive);
  }, [popupActive]);

  const handleX = () => {
    setPopupActive(!popupActive);
  };

  return (
    <div
      style={{
        visibility: popupActive ? 'visible' : 'hidden',
        opacity: popupActive ? '1' : '0',
      }}
    >
      <div>
        <div>{props.children}</div>
        <button data-testid="button-popup" onClick={handleX}>
          Got It
        </button>
      </div>
    </div>
  );
};

export default Popup;

index.test.tsx:

import { fireEvent, render, screen } from '@testing-library/react';
import '@testing-library/jest-dom/extend-expect';
import React from 'react';
import Popup from './';

describe('73407176', () => {
  test('should pass', () => {
    render(
      <Popup>
        <div id="content"></div>
      </Popup>
    );

    const button = screen.getByText('Got It');
    fireEvent.click(button);
    expect(button).not.toBeVisible();
  });
});

Test result:

 PASS  stackoverflow/73407176/index.test.tsx (11.549 s)
  73407176
    ✓ should pass (73 ms)

-----------|---------|----------|---------|---------|-------------------
File       | % Stmts | % Branch | % Funcs | % Lines | Uncovered Line #s 
-----------|---------|----------|---------|---------|-------------------
All files  |     100 |    83.33 |     100 |     100 |                   
 index.tsx |     100 |    83.33 |     100 |     100 | 8                 
-----------|---------|----------|---------|---------|-------------------
Test Suites: 1 passed, 1 total
Tests:       1 passed, 1 total
Snapshots:   0 total
Time:        12.167 s

Also check this question: What is the difference between toBeInTheDocument() and toBeVisible()?