chore: migrate from Turbo to Bun workspace commands (#192)

## Summary

Migrate the monorepo build system from Turbo to Bun's native workspace
commands. This removes unnecessary dependencies and simplifies the build
tooling stack.

## What Changed

- **Build commands**: Replaced all `turbo run` commands with `bun run
--filter '*'` equivalents in package.json scripts
- **Dependencies removed**:
  - `turbo`: No longer needed with Bun's native workspace support
  - `husky`: Git hooks removed from the workflow
  - `lint-staged`: Formatting now handled by CI pipeline
- **Configuration**: Deleted turbo.json file
- **Bun version**: Updated from 1.2.18 to 1.3.2
- **Package.json cleanup**: Removed lint-staged configuration

## Why

- **Simpler tooling**: Bun provides native monorepo support, eliminating
the need for Turbo
- **Fewer dependencies**: Reduces complexity and maintenance overhead
- **Faster CI/CD**: Leverages Bun's optimised workspace handling
- **Cleaner configuration**: Removes intermediate configuration files

All functionality is preserved - the monorepo continues to work exactly
as before, just with simpler tooling.



<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Switch the monorepo from Turbo to Bun workspace commands. This
simplifies the build and removes extra dependencies without changing
behavior.

- **Refactors**
- Replace `turbo run` with `bun run --filter '*'` for start, server,
dev, build, test, typecheck.
  - Delete turbo.json and the `prepare` script.
  - Remove lint-staged config from package.json.

- **Dependencies**
  - Remove turbo, husky, lint-staged.
  - Update packageManager to [email protected].

<sup>Written for commit 4839ea1.
Summary will update automatically on new commits.</sup>

<!-- End of auto-generated description by cubic. -->

Author: ryoppippi