Run Automation testcase from TestPlan having multiple test configuration assigned

How about using RunAutomatedTest API:

1. Use the RunAutomatedTest API
- Query all test points for the test case using the Test Point API.
- For each test point (i.e., each configuration), trigger a test run using the Run Create API.
- This ensures each configuration instance is executed independently.
2. Use YAML Pipeline with Test Plan Integration
If you're using a release pipeline, you can integrate with Azure Test Plans using the VsTest task:

- task: VSTest@2
  inputs:
    testSelector: 'testPlan'
    testPlan: '<TestPlanId>'
    testSuite: '<TestSuiteId>'
    testConfiguration: '<ConfigurationId>'
    searchFolder: '$(System.DefaultWorkingDirectory)'

To run multiple configurations, you can loop through them or define multiple VSTest tasks with different testConfiguration values.