Invalid client_session entity with multiple trackers

Describe the bug
When using two trackers(A and B) on the same page and tracker A have configured:

anonymousTracking: {
    withSessionTracking: true,
}

tracker B attaches an invalid client_session entity (iglu:com.snowplowanalytics.snowplow/client_session/jsonschema/1-0-2) to all events. The entity is invalid due to the userId is empty string.
Tracker A sets a valid client_session entity with userId : "00000000-0000-0000-0000-000000000000"

To Reproduce

• Initialize two trackers from v4 package on a simple webpage:

import { newTracker, trackPageView } from '@snowplow/browser-tracker';

const tracker_a = newTracker('tracker_a', 'https://a.example.com', {
  appId: 'my-app',
  contexts: {
    session: true,
  },
  anonymousTracking: {
    withSessionTracking: true,
  },
});

const tracker_b = newTracker('tracker_b', 'https://b.example.com', {
    appId: 'my-app',
    contexts: {
      session: true,
    },
  });

  trackPageView();

• Load the webpage in a browser

Expected behavior
Two page views send with the client_session entity attached. Both of them should be valid.

Actual behaviour
Two page views send with the client_session entity attached. tracker_b's client_session entity is invalid because userId is empty string.

Screenshots
If applicable, add screenshots to help explain your problem.

Desktop (please complete the following information):

• OS: Windows 11
• Browser: Edge
• Version 130.0.2849.68

Smartphone (please complete the following information):

• Device: [e.g. iPhone6]
• OS: [e.g. iOS8.1]
• Browser [e.g. stock browser, safari]
• Version [e.g. 22]

Additional context
If setting the cookieName to different values on the two trackers this bug seems to go away.

Start by reproducing the two-tracker example from the issue with shared cookie settings, then inspect how each tracker creates and attaches its client_session entity. Verify the fix by confirming both page-view events contain valid entities, including a non-empty userId for tracker B.