If you are using react-testing-library, then this also will work:
expect(component.queryByText("Text I care about").toBeNull());
expect(within(component).queryByText("Text I care about")).toBeNull();
Note: In my case, I needed to use queryBy* because it doesn´t error out when the text element (that contains the text: Text I care about) does not exist. Therefore, I could evaluate whether there is an existence of a text component or not.