Add unit tests for critical logic in Typescript package

Description:

Currently, there are no apparent automated tests for the run-gemini-cli action. To ensure the reliability and correctness of the action, comprehensive test coverage is required, especially for the critical logic branches identified during refactoring.

Depends on https://github.com/google-github-actions/run-gemini-cli/issues/373

Specific testing requirements:

1. Unit Tests for TypeScript Modules:
   • Develop unit tests for all functions and modules created during the refactoring process (e.g., input validation, installation logic, telemetry upload).
   • Achieve high code coverage for these modules, focusing on all conditional branches and edge cases.
2. Mocking External Dependencies:
   • Mock external calls (e.g., npm, git, docker, curl, gemini CLI) to ensure unit tests are fast and isolated.

Acceptance Criteria:

• A testing framework is integrated into the project.
• Unit tests are written for all refactored TypeScript modules.
• Test coverage reports demonstrate significant coverage of the action's core logic.
• Tests can be run easily via a npm script.

Start by reviewing the refactoring tracked in issue 373 and identify the TypeScript modules and critical branches it introduced, including input validation, installation logic, and telemetry upload. Choose a testing framework, mock the listed external calls, and add an npm script to run the tests. Done means the refactored modules have significant branch coverage and produce a coverage report.