Enable Lighthouse CI App integration for nicer checks display?

Currently the lighthouse result show up as:

>
>
> Total size of all the files uploaded is 1165820 bytes
> Finished uploading artifact lighthouse-results. Reported size is 1165820 bytes. There were 0 items that failed to upload
> Uploading median LHR of http://localhost:45821/about.html...success!
> Open the report at https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813497053-27107.report.html
> Uploading median LHR of http://localhost:45821/binder.html...success!
> Open the report at https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813497456-16487.report.html
> Uploading median LHR of http://localhost:45821/community.html...success!
> Open the report at https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813497852-78305.report.html
> Uploading median LHR of http://localhost:45821/documentation.html...success!
> Open the report at https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813498306-7357.report.html
> Uploading median LHR of http://localhost:45821/hub.html...success!
> Open the report at https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813498846-65386.report.html
> No GitHub token set, skipping GitHub status check.
> Dumping 5 reports to disk at /home/runner/work/jupyter.github.io/jupyter.github.io/.lighthouseci...
> Done writing reports to disk.
>
>
>
>
> Error: 2 results for http://localhost:45821/about.html
> Report: https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813497053-27107.report.html
>
> ❌ `categories.accessibility` failure for `minScore` assertion
> Expected >= 0.95, but found 0.94
>
> ❌ `categories.best-practices` failure for `minScore` assertion
> Expected >= 0.95, but found 0.93
> Error: 2 results for http://localhost:45821/binder.html
> Report: https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813497456-16487.report.html
>
> ❌ `categories.accessibility` failure for `minScore` assertion
> Expected >= 0.95, but found 0.85
>
> ❌ `categories.seo` failure for `minScore` assertion
> Expected >= 0.95, but found 0.92
> Error: 1 result for http://localhost:45821/documentation.html
> Report: https://storage.googleapis.com/lighthouse-infrastructure.appspot.com/reports/1640813498306-7357.report.html
>
> ❌ `categories.accessibility` failure for `minScore` assertion
> Expected >= 0.95, but found 0.94

But we could go fancy and have:


This would require authorizing https://github.com/apps/lighthouse-ci ; it is tied to a private account of maintainer but also mentioned on https://github.com/GoogleChrome/lighthouse-ci/blob/main/docs/getting-started.md#github-status-checks.

Just an option - I don't have opinion on this one.

_Originally posted by @krassowski in https://github.com/jupyter/jupyter.github.io/issues/579#issuecomment-1002793724_

Start with the Lighthouse CI GitHub status checks documentation linked in the issue and inspect the repository's existing CI configuration that produces the Lighthouse output. Determine the required GitHub App authorization and configuration, then verify that checks display the reported Lighthouse failures without exposing maintainer credentials.

Written by the indexing model from the issue text.