fix: drop removed APIs

[isha689]

Fixes

• Drop shortcuts for removed APIs. Ref: here
• Fix casing for TaskrouterBase
• Add Api property to BaseClient

  Checklist

• [x] I acknowledge that all my contributions will be made under the project's license
• [ ] I have made a material change to the repo (functionality, testing, spelling, grammar)
• [ ] I have read the Contribution Guidelines and my PR follows them
• [ ] I have titled the PR appropriately
• [ ] I have updated my branch with the main branch
• [ ] I have added tests that prove my fix is effective or that my feature works
• [ ] I have added the necessary documentation about the functionality in the appropriate .md file
• [ ] I have added inline documentation to the code I modified

If you have questions, please file a support ticket, or create a GitHub Issue in this repository.