supabase-ssr: Failed to execute 'postMessage' on 'BroadcastChannel'

[Aietes]

Bug report

• I confirm this is a bug with Supabase, not with my own application.
• I confirm I have searched the Docs, GitHub Discussions, and Discord.

Describe the bug

Using the supabase-ssr library with Nuxt 3, I'm getting the following error:

DOMException: Failed to execute 'postMessage' on 'BroadcastChannel': #<Object> could not be cloned.
    at SupabaseAuthClient._notifyAllSubscribers (http://localhost:3000/_nuxt/node_modules/.cache/vite/client/deps/chunk-A274CJAX.js?v=7251ccc1:2156:31)
    at SupabaseAuthClient._recoverAndRefresh (http://localhost:3000/_nuxt/node_modules/.cache/vite/client/deps/chunk-A274CJAX.js?v=7251ccc1:2101:20)
    at async http://localhost:3000/_nuxt/node_modules/.cache/vite/client/deps/chunk-A274CJAX.js?v=7251ccc1:2351:11

I'm trying to pin down where the error comes from, it could be related to serializing cookies. I hope to get help, determine if this error has an impact on auth, and ideally fix it.

To Reproduce

Steps to reproduce the behavior, please provide code snippets or a repository:

I'll try to provide a reproduction, but since this error is auth related, I can't provide the actual code base.

Expected behavior

No postMessage / broadcast error to occur.

Screenshots

System information

Operating System: Linux
Node Version: v18.18.0
Nuxt Version: 3.9.3
CLI Version: 3.10.0
Nitro Version: 2.8.1
Package Manager: npm@10.2.3

Additional context

Add any other context about the problem here.