Migrate from bun to npm, pnpm, or yarn as the package manager

[shige]

Task description

Migrate from bun to npm, pnpm, or yarn as the package manager.

Background

• It's inconvenient that I can't check the differences on a GitHub pull request and also can't provide the context to the Copilot Extension for review.
• This task is necessary because currently, using bun:test with mock.module does not provide a way to reset the mocks.

Transitioning to npm, pnpm, or yarn will allow for more flexibility and might resolve the limitations encountered with bun.

TODO (Optional)

• Evaluate and choose between npm, pnpm, or yarn.
• Remove bun from the project and install the new package manager.
• Update the project's dependency management scripts to use the new package manager.

Additional notes (Optional)

[toyamarinyon]

I was the one who adopted Bun, and I currently think we should migrate to npm, so I'll write down my thoughts.

First, the initial issue mentioned in the background is resolved by Bun v1.1.39, which enables text-based lock files.

https://x.com/bunjavascript/status/1866879040424120625

However, Bun is not being used as widely as I had imagined. In particular, most publicly available OSS applications that developers can try out immediately use npm or pnpm.

Vercel example (pnpm): https://github.com/vercel/ai-chatbot
OpenAI example (npm): https://github.com/openai/openai-realtime-console
Supabase example (npm): https://github.com/supabase-community/database-build

If this trend doesn't change, I believe switching from Bun to npm (or pnpm) would be a better choice for developers.