Refactor: Update workflow, script, and tests for latest integration test action

[magajh]

… version for integration tests

Description

Describe what this pull request changes, and why. Include implications for people using this change.

Useful information to include:

• Which user roles will this change impact? Common user roles are "Learner", "Course Author",
  "Developer", and "Operator".
• Include screenshots for changes to the UI (ideally, both "before" and "after" screenshots, if applicable).
• Provide links to the description of corresponding configuration changes. Remember to correctly annotate these
  changes.

Testing instructions

Please provide detailed step-by-step instructions for testing this change.

Additional information

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• Does this change depend on other changes elsewhere?
• Any special concerns or limitations? For example: deprecations, migrations, security, or accessibility.
• Link to other information about the change, such as Jira issues, GitHub issues, or Discourse discussions.

Checklist for Merge

• Tested in a remote environment
• Updated documentation
• Rebased master/main
• Squashed commits