The correct option is Checks API.

The Checks API is designed for integrations to create and update check runs that are attached to specific commits, which makes their results visible on pull requests and commit pages. It supports in depth reporting through statuses like queued, in progress, and completed, as well as conclusions and rich output that includes titles, summaries, text, and annotations. This lets an integration surface job outcomes and log details directly in the pull request Checks tab and in the commit UI.

Actions API is not appropriate for this need because it focuses on managing workflow runs, jobs, and artifacts. It does not provide a way to author check runs or annotate commits so it cannot directly publish detailed check results to pull requests.

Audit Log API records organization and enterprise events for security and compliance. It does not publish build or test results to commits or pull requests and therefore does not meet the requirement.

Statuses API only sets a simple state on a commit such as pending, success, or failure with an optional description and link. It does not support rich summaries, annotations, or detailed log content, so it cannot deliver the level of information described in the prompt.

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