[JENKINS-75574] Fix "No builds" remaining after first build

[Vlatombe]

Amends #10309

See JENKINS-75574.

Testing done

Checked that the scenario described in the jira behaves as expected now.

Proposed changelog entries

• Fix "No builds" remaining after first build

Proposed changelog category

/label

Proposed upgrade guidelines

N/A

Submitter checklist

• The Jira issue, if it exists, is well-described.
• The changelog entries and upgrade guidelines are appropriate for the audience affected by the change (users or developers, depending on the change) and are in the imperative mood (see examples). Fill in the Proposed upgrade guidelines section only if there are breaking changes or changes that may require extra steps from users during upgrade.
• There is automated testing or an explanation as to why this change has no tests.
• New public classes, fields, and methods are annotated with @Restricted or have @since TODO Javadocs, as appropriate.
• New deprecations are annotated with @Deprecated(since = "TODO") or @Deprecated(forRemoval = true, since = "TODO"), if applicable.
• New or substantially changed JavaScript is not defined inline and does not call eval to ease future introduction of Content Security Policy (CSP) directives (see documentation).
• For dependency updates, there are links to external changelogs and, if possible, full differentials.
• For new APIs and extension points, there is a link to at least one consumer.

Desired reviewers

@mention

Before the changes are marked as ready-for-merge:

Maintainer checklist

• There are at least two (2) approvals for the pull request and no outstanding requests for change.
• Conversations in the pull request are over, or it is explicit that a reviewer is not blocking the change.
• Changelog entries in the pull request title and/or Proposed changelog entries are accurate, human-readable, and in the imperative mood.
• Proper changelog labels are set so that the changelog can be generated automatically.
• If the change needs additional upgrade steps from users, the upgrade-guide-needed label is set and there is a Proposed upgrade guidelines section in the pull request title (see example).
• If it would make sense to backport the change to LTS, a Jira issue must exist, be a Bug or Improvement, and be labeled as lts-candidate to be considered (see query).

[timja]

/label ready-for-merge

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This PR is now ready for merge, after ~24 hours, we will merge it if there's no negative feedback.

Thanks!

[A1exKH]

LGTM.