Custom "details" link in the github pr checks

I believe they are coming from an external source and not GitHub Actions. If you are using GitHub Actions I do not think this is feasible.

You can however create a deployment environment and add the url parameter to it so you can click the "View Deployment" button.

https://docs.github.com/en/actions/deployment/targeting-different-environments/using-environments-for-deployment#using-an-environment

You can create a custom check for your PR using the GitHub REST API. In particular, you want to look at Checks - Create a check run. Part of the payload for that endpoint is a field called details_url where you can specify the URL.

Sample API call with curl:

curl \
  -X POST \
  -H "Accept: application/vnd.github.v3+json" \
  https://api.github.com/repos/octocat/hello-world/check-runs \
  -d '{"name":"name","head_sha":"head_sha", "details_url": "https://my-custom-url.com"}'

Seems the GitHub Actions: checks-action is a good fix to solve your problem:

jobs:
  test_something:
    runs-on: ubuntu-latest
    steps:
    - uses: actions/checkout@v1
    - uses: actions/create-outputs@v0.0.0-fake
      id: test
    - uses: LouisBrunner/checks-action@v1.1.1
      if: always()
      with:
        token: ${{ secrets.GITHUB_TOKEN }}
        name: Test XYZ
        conclusion: ${{ job.status }}
        output: |
          {"summary":${{ steps.test.outputs.summary }}}

The output field could help:

output:
Supports the following properties:

summary: Required, summary of your check
text_description: Optional, a text description of your annotation (if any)

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