Centralize Pipeline Analysis Next Steps and Auto Fix workflows in azure-sdk-tools

Currently, both the [pipeline analysis](https://github.com/Azure/azure-sdk-for-python/blob/main/.github/workflows/pipeline-analysis-next-steps.md) and [automatic fix](https://github.com/Azure/azure-sdk-for-python/blob/main/.github/workflows/pipeline-analysis-auto-fix.md) GitHub Agentic Workflows are implemented in the `azure-sdk-for-python` repository. Both .md and .lock.yml files should be moved into the `azure-sdk-tools/.github/workflows` folder.

After completing the JavaScript modularization in [this issue](https://github.com/Azure/azure-sdk-tools/issues/16930), the required src modules should also be maintained and synced within the `azure-sdk-tools` repository.

**Success Criteria**
- `azure-sdk-tools` should be the main source for both workflows, their corresponding lock files, and their corresponding JavaScript src and test files.
- The common sync workflow should include specified workflows, their corresponding lock files, and their corresponding JavaScript src files.
- Common test files should only exist in the `azure-sdk-tools` repository with a corresponding pipeline to run the JavaScript tests.