From DOM Testing-library Docs - Appearance and Disappearance

Asserting elements are not present

The standard getBy methods throw an error when they can't find an element, so if you want to make an assertion that an element is not present in the DOM, you can use queryBy APIs instead:

const submitButton = screen.queryByText('submit')
expect(submitButton).toBeNull() // it doesn't exist

The queryAll APIs version return an array of matching nodes. The length of the array can be useful for assertions after elements are added or removed from the DOM.

const submitButtons = screen.queryAllByText('submit')
expect(submitButtons).toHaveLength(2) // expect 2 elements

not.toBeInTheDocument

The jest-dom utility library provides the .toBeInTheDocument() matcher, which can be used to assert that an element is in the body of the document, or not. This can be more meaningful than asserting a query result is null.

import '@testing-library/jest-dom/extend-expect'
// use `queryBy` to avoid throwing an error with `getBy`
const submitButton = screen.queryByText('submit')
expect(submitButton).not.toBeInTheDocument()

Use queryBy / queryAllBy.

As you say, getBy* and getAllBy* throw an error if nothing is found.

However, the equivalent methods queryBy* and queryAllBy* instead return null or []:

queryBy

queryBy* queries return the first matching node for a query, and return null if no elements match. This is useful for asserting an element that is not present. This throws if more than one match is found (use queryAllBy instead).

queryAllBy queryAllBy* queries return an array of all matching nodes for a query, and return an empty array ([]) if no elements match.

https://testing-library.com/docs/dom-testing-library/api-queries#queryby

So for the specific two you mentioned, you'd instead use queryByText and queryByTestId, but these work for all queries, not just those two.

getBy* throws an error when not finding an elements, so you can check for that

expect(() => getByText('your text')).toThrow('Unable to find an element');