Supabase adaptor show error when integrate with AWS Cognito Provider

[willy20040711]

Adapter type

@auth/supabase-adapter

Environment

  System:
    OS: Linux 5.15 Ubuntu 20.04.6 LTS (Focal Fossa)
    CPU: (20) x64 13th Gen Intel(R) Core(TM) i7-13700H
    Memory: 1.65 GB / 7.64 GB
    Container: Yes
    Shell: 5.0.17 - /bin/bash
  Binaries:
    Node: 20.18.0 - ~/.nvm/versions/node/v20.18.0/bin/node
    Yarn: 4.5.1 - ~/.nvm/versions/node/v20.18.0/bin/yarn
    npm: 10.8.2 - ~/.nvm/versions/node/v20.18.0/bin/npm
  npmPackages:
    @auth/supabase-adapter: ^1.7.4 => 1.7.4 
    @auth/unstorage-adapter: ^2.0.0 => 2.7.4 
    next: latest => 15.1.4 
    next-auth: beta => 5.0.0-beta.25 
    react: ^18.2.0 => 18.3.1 

Reproduction URL

https://github.com/willy20040711/test_nextauth

Describe the issue

I try to use nextauth to integrate aws coginto with supabase adaptor.
Shows adaptor error as below, not pretty sure if getUserByAccount method cause this error:

[auth][debug]: adapter_getUserByAccount {
  "args": [
    {
      "providerAccountId": "492a858c-c001-70ef-01c2-6e603c8bc40e",
      "provider": "cognito"
    }
  ]
}
[auth][error] AdapterError: Read more at https://errors.authjs.dev#adaptererror
    at acc.<computed> (webpack-internal:///(rsc)/./node_modules/next-auth/node_modules/@auth/core/lib/init.js:177:31)
    at process.processTicksAndRejections (node:internal/process/task_queues:95:5)
    at async Module.callback (webpack-internal:///(rsc)/./node_modules/next-auth/node_modules/@auth/core/lib/actions/callback/index.js:68:33)
    at async AuthInternal (webpack-internal:///(rsc)/./node_modules/next-auth/node_modules/@auth/core/lib/index.js:43:24) 

How to reproduce

in my Reproduction URL click sigin in localhost:3001, need to add some env var.

Expected behavior

Login in sucess.