Users are not getting logged out across tabs on web

[Mr-Pepe]

Describe the bug
Currently, logging a user out in one tab of a web browser does not log the user out in other tabs.

To Reproduce

1. Log in in one tab
2. Open a second tab -> The user is logged in in the second tab
3. Log out in the first tab -> An AuthChangeEvent.signedOut event is triggered in the first tab but not in the second tab

Actions that require a signed-in user are still possible in the second tab.

Expected behavior

The sign-out event should get triggered in all tabs.

Version (please complete the following information):
├── supabase_flutter 2.5.5
│ ├── supabase 2.2.1
│ │ ├── functions_client 2.2.0
│ │ ├── gotrue 2.8.0
│ │ ├── postgrest 2.1.2
│ │ ├── realtime_client 2.1.0
│ │ ├── storage_client 2.0.2