[Nov 15th] Update docs for integration-specific status checks (#22507)

* Update docs for integration-specific status checks

github/docs-content#5379

* Use dynamic product names.

* Update required status list screenshot.

* Update content/repositories/configuring-branches-and-merges-in-your-repository/defining-the-mergeability-of-pull-requests/troubleshooting-required-status-checks.md

Co-authored-by: hubwriter <hubwriter@github.com>

* Update managing-a-branch-protection-rule.md

Co-authored-by: hubwriter <hubwriter@github.com>
Co-authored-by: Felicity Chapman <felicitymay@github.com>

Author: 3 people

assets/images/help/repository/required-statuses-list.png

@@ -87,11 +87,7 @@ Before you can enable required status checks, you must configure the repository
 
 After enabling required status checks, all required status checks must pass before collaborators can merge changes into the protected branch. After all required status checks pass, any commits must either be pushed to another branch and then merged or pushed directly to the protected branch.
 
-{% note %}
-
-**Note:** Any person or integration with write permissions to a repository can set the state of any status check in the repository. {% data variables.product.company_short %} does not verify that the author of a check is authorized to create a check with a certain name or modify an existing status. Before merging a pull request, you should verify that the author of each status, listed in the merge box, is expected.
-
-{% endnote %}
+Any person or integration with write permissions to a repository can set the state of any status check in the repository, but in some cases you may only want to accept a status check from a specific {% data variables.product.prodname_github_app %}. When you add a required status check, you can select an app that has recently set this check as the expected source of status updates. If the status is set by any other person or integration, merging won't be allowed. If you select "any source", you can still manually verify the author of each status, listed in the merge box.
 
 You can set up required status checks to either be "loose" or "strict." The type of required status check you choose determines whether your branch is required to be up to date with the base branch before merging.
 

content/repositories/configuring-branches-and-merges-in-your-repository/defining-the-mergeability-of-pull-requests/about-protected-branches.md

@@ -69,13 +69,13 @@ When you create a branch rule, the branch you specify doesn't have to exist yet
      ![Require review from code owners](/assets/images/help/repository/PR-review-required-code-owner.png)
    - Optionally, if the repository is part of an organization, select **Restrict who can dismiss pull request reviews**. Then, search for and select the people or teams who are allowed to dismiss pull request reviews. For more information, see "[Dismissing a pull request review](/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/dismissing-a-pull-request-review)."
      ![Restrict who can dismiss pull request reviews checkbox](/assets/images/help/repository/PR-review-required-dismissals.png)
-1. Optionally, enable required status checks.
+1. Optionally, enable required status checks. For more information, see "[About status checks](/pull-requests/collaborating-with-pull-requests/collaborating-on-repositories-with-code-quality-features/about-status-checks)."
    - Select **Require status checks to pass before merging**.
      ![Required status checks option](/assets/images/help/repository/required-status-checks.png)
    - Optionally, to ensure that pull requests are tested with the latest code on the protected branch, select **Require branches to be up to date before merging**.
      ![Loose or strict required status checkbox](/assets/images/help/repository/protecting-branch-loose-status.png)
-   - From the list of available status checks, select the checks you want to require.
-     ![List of available status checks](/assets/images/help/repository/required-statuses-list.png)
+   - Search for status checks, selecting the checks you want to require.
+     ![Search interface for available status checks, with list of required checks](/assets/images/help/repository/required-statuses-list.png)
 {%- ifversion fpt or ghes > 3.1 or ghae-issue-4382 %}
 1. Optionally, select **Require conversation resolution before merging**.
   ![Require conversation resolution before merging option](/assets/images/help/repository/require-conversation-resolution.png)

content/repositories/configuring-branches-and-merges-in-your-repository/defining-the-mergeability-of-pull-requests/managing-a-branch-protection-rule.md

@@ -42,3 +42,9 @@ Sometimes, the results of the status checks for the test merge commit and head c
 
 ![Branch with conflicting merge commits](/assets/images/help/repository/req-status-check-conflicting-merge-commits.png)
 {% endif %}
+
+It's also possible for a protected branch to require a status check from a specific {% data variables.product.prodname_github_app %}. If you see a message similar to the following, then you should verify that the check listed in the merge box was set by the expected app.
+
+```
+Required status check "build" was not set by the expected {% data variables.product.prodname_github_app %}.
+```