React SDK running on NextJS (SSR) cannot recognize login through separate domain

Using the React SDK v1.10.2 on Next.js v12.3.1

Our main site is running NextJS with the Auth0 React SDK (this is because we do not want the server to be performing the authentication calls due to overhead). If we initiate a login through the main site, when the user returns to the site, they are recognized as logged in. However, if the user initiates the login from a secondary site, then visits the main site, they are not recognized as being logged in. Additionally, attempts to fetch the token (without cache) fail.

I believe this has to do with the React SDK being instantiated during the server-side rendering. How do I get it to instantiate in the browser?

(Other sites at separate domains using just React w/ w the Auth0 React SDK perform as expected)