Question: What is the best way to use this library within a Web Worker?

I've been trying to use this library to fetch resources within the browser via a Web Worker, without much success.
I will describe below what I have tried up until now, and was wondering if someone could give me some pointers on what would be the best way to go forward.

My intended workflow:

1. Authenticate the user within the browser itself.
2. Serialize the session and send it to the Worker within a message.
3. Deserialize the session within the Worker.
4. Do fetch requests using the authenticated session.

Step 1 works without problems, but I'm unsure how to handle steps 2-3.
So far, I tried two approaches:

Serialization attempt 1

Main browser process:

// session is authenticated at this stage
const sessionInfoRaw = session.clientAuthentication.getSessionInfo(session.info.sessionId);
sendToWorker(sessionInfoRaw);

(I am aware that session.clientAuthentication is private, so this is probably not a good solution)

Worker:

const session = new Session({ sessionInfo: sessionInfoRaw });
await session.login({});

=> Throws a window is not defined error at BrowserStorage.js:5 (possibly caused by #308).

I can observe that the session already contains the correct webId value.

Serialization attempt 2

Main browser process:

// session is authenticated at this stage
const sessionInfoRaw = session.clientAuthentication.getSessionInfo(session.info.sessionId);
sendToWorker({
  refreshToken: sessionInfoRaw.refreshToken,
  clientId: sessionInfoRaw.clientAppId,
  clientSecret: sessionInfoRaw.clientAppSecret,
  oidcIssuer: sessionInfoRaw.issuer,
});

Worker:

const session = new Session();
await session.login(sessionInfoRaw);

=> Throws a window is not defined error at BrowserStorage.js:5 (possibly caused by #308).

In this case, the session contains an undefined webId value.

Start at BrowserStorage.js:5 and trace the Session constructor and login paths used by the worker examples. Compare both serialized-session approaches with the browser authentication flow and the Web Worker environment. Done means identifying a supported way to authenticate and issue fetch requests from a worker, or documenting the missing support.