VIDEO-13047 Fix build errors for TypeScript 5.x.

[manjeshbhargav]

Contributing to Twilio

All third party contributors acknowledge that any contributions they provide will be made under the same open source license that the open source project is provided under.

• [x] I acknowledge that all my contributions will be made under the project's license.

Pull Request Details

Description

• [x] Fix build errors for TypeScript 5.x
• [x] Fix documentation generation

Burndown

Before review

• [x] Updated CHANGELOG.md if necessary
• [ ] Added unit tests if necessary
• [x] Updated affected documentation
• [x] Verified locally with npm test
• [x] Manually sanity tested running locally
• [ ] Included screenshot as PR comment (if needed)
• [x] Ready for review

[manjeshbhargav]

@charliesantos The one thing that I may need your help with is the fact that migrating to TypeScript 5.x and upgrading TypeDoc results in the generated docs not having exports.