You can set the session using localStorage and thus, it can be accessed by any app within your browser, until you or the logout operation clears the session.
What kind of session do you mean? Is it an AEM user session? If so, this is going to depend on how your React app is integrated with AEM. Is it being served by AEM ? If so, it should be able to access the session easily since the browser holds the session.
You can set the session using localStorage and thus, it can be accessed by any app within your browser, until you or the logout operation clears the session.