This is possible.
Your webserver would serve the react app for the /auth/* route, and for other routes, it would server the vue app.
The react app would use supertokens-auth-react SDK. The Vue app would use supertokens-website SDK (which is also used inside supertokens-auth-react).
Upon login, the session tokens will be stored in the cookies and attached to the API domain + the website domain. So you don't need to do anything special to communicate between the react and vue app.