Is there a context in oAuth, reusable in the callback?

The state parameter: https://auth0.com/docs/secure/attack-protection/state-parameters

You can use the state parameter to encode an application state that will put the user where they were before the authentication process started. For example, if a user intends to access a protected page in your application, and that action triggers the request to authenticate, you can store that URL to redirect the user back to their intended page after the authentication finishes.

Generate and store a nonce locally (in cookies, session, or local storage) along with any desired state data like the redirect URL. Use the nonce as a state in the protocol message. If the returned state matches the stored nonce, accept the OAuth2 message and fetch the corresponding state data from storage. This is the approach we use in auth0.js.