Private ECR credentials are not passed from first job to second job

[joosangkim]

Describe the bug
Following this document, I want to launch a job on a container from my private ECR repository on self-hosted runner(dind mode in k8s).
However there is no basic auth credentials error from second job.

action yaml

name:  "test"
on:
  push:
    branch: action-test
jobs:
  login-to-ecr:
    permissions:
      contents: read
      issues: read
      id-token: write
      checks: write
      pull-requests: write
    runs-on: [ arc-runner-dind ]
    steps:
      - name: Get AWS Credentials
         uses: aws-actions/configure-aws-credentials@v2
         with:
            aws-region: ap-northeast-2
            role-to-assume: MY-TEST-ROLE
            role-session-name:  MY-TEST-ROLE-SESSION
            mask-aws-account-id: false
      - name: Login to Amazon ECR
        id: login-ecr
        uses: aws-actions/amazon-ecr-login@v2
        with:
          mask-password: false
          skip-logout: true
      - name: test
        run: |
          docker pull 000000000000.dkr.ecr.ap-northeast-2.amazonaws.com/actions-runner-image:lastest
      - name: echo
        run: |
          echo "${{ steps.login-ecr.outputs.docker_username_000000000000_dkr_ecr_ap_northeast_2_amazonaws_com }}"
          echo "${{ steps.login-ecr.outputs.docker_password_000000000000_dkr_ecr_ap_northeast_2_amazonaws_com }}"
    outputs:
      docker_username: ${{ steps.login-ecr.outputs.docker_username_000000000000_dkr_ecr_ap_northeast_2_amazonaws_com }}
      docker_password: ${{ steps.login-ecr.outputs.docker_password_000000000000_dkr_ecr_ap_northeast_2_amazonaws_com }}

  CI-Test:
    permissions:
      contents: read
      issues: read
      id-token: write
      checks: write
      pull-requests: write
    runs-on:  [ arc-runner-dind ]
    needs: login-to-ecr
    container:
      image: 000000000000.dkr.ecr.ap-northeast-2.amazonaws.com/actions-runner-image:latest
      options: --pull=always
      credentials:
        username: ${{ needs.login-to-ecr.outputs.docker_username }}
        password: ${{ needs.login-to-ecr.outputs.docker_password }}
    steps:
      - name: test
        run: |
          echo "hello"

Pulling a private ECR image from login-to-ecr has no issue however pulling same image as a job container from CI-Test job got failed with Error response from daemon: Head "https://000000000000.dkr.ecr.ap-northeast-2.amazonaws.com/v2/actions-runner-image/manifests/latest": no basic auth credentials

To Reproduce
Steps to reproduce the behavior:

• AWS private ECR login in first job and pass credentials as outputs to <job>.container.credentials to second job.

Expected behavior
A job on a container from private ECR repo should be launched on self-hosted runner.

Screenshots
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Desktop (please complete the following information):

• OS: EKS 1.28 / dind mode arc(action runner controller)

Additional context
Add any other context about the problem here.