feat!: migrate vite ecosystem toolchain to Vite+

[jong-kyung]

Summary

This migration gives the monorepo one Vite+ entry point for installation, builds, tests, formatting, linting, task orchestration, and CI while preserving pnpm 9.15.0.

Key decisions

• Package Vite configurations now share build and test settings, replacing separate tsup and Vitest configuration files.
• Vite Task replaces Turbo for recursive workspace execution and local caching.
• pnpm graph overrides keep every package on the Vite and Vitest versions managed by Vite+.
• Existing ESLint and Husky workflows remain because ESLint 8 cannot be migrated automatically to the ESLint 9 flat configuration.

Validation

• vp install
• vp check
• vp run build
• vp run test
• vp run test:integration: 7 files and 53 tests passed
• vp run lint
• vp run type-check

closes #4

[jong-kyung]

@codex review

[jong-kyung]

IMO, we also need to upgrade pnpm v9 to v11

[jong-kyung]

CI fails on Node 20 because the bundled tsdown version requires Node.js ^22.18.0. I couldn't reproduce the issue initially because the project doesn't specify a version in .node-version 😢

[Kyujenius]

@jong-kyung
Let's keep this PR scoped to the toolchain. pnpm 9→11 touches the lockfile format and packageManager independently,
I'll take it! Thanks

[Kyujenius]

@jong-kyung
I set up -vp's cache: true only persists the dependency store — the Vite Task cache was starting empty on every CI run, so tasks always rebuilt. 846d2a5 adds explicit restore/save steps per the official GitHub Actions Cache guide