ci: run docker build checks

[ferrarimarco]

Proposed changes

Run docker build checks as part of the test suite.

Ref https://docs.docker.com/reference/build-checks/

Readiness checklist

In order to have this pull request merged, complete the following tasks.

Pull request author tasks

• I checked that all workflows return a success.
• I included all the needed documentation for this change.
• I provided the necessary tests.
• I squashed all the commits into a single commit.
• I followed the Conventional Commit v1.0.0 spec.
• I wrote the necessary upgrade instructions in the upgrade guide.
• If this pull request is about and existing issue,
  I added the Fix #ISSUE_NUMBER or Close #ISSUE_NUMBER text to the description of the pull request.

Super-linter maintainer tasks

• Label as breaking if this change breaks compatibility with the previous released version.
• Label as either: automation, bug, documentation, enhancement, infrastructure.
• Add the pull request to a milestone, eventually creating one, that matches with the version that release-please proposes.

[ferrarimarco]

/cc @harryzcy

[ferrarimarco]

#5862 should unblock this.