chore(tooling): migrate to Vite+

[caiopizzol]

Vite+ consolidates formatting, linting, type checking, tests, package installation, and staged checks behind one pinned toolchain. This follow-up builds on the TypeScript 7 baseline from #12 and removes overlapping tool ownership.

• Accepts generated formatter defaults, so the review includes repository-wide formatting changes.
• Keeps Bun as the pipeline runtime while Vite+ owns development checks and Vitest.
• Keeps production installs safe when development dependencies and hook tooling are omitted.
• Leaves deployment on Bun source because this pipeline has no Vite application build entry.

[cubic-dev-ai]

No issues found across 26 files

_{Re-trigger cubic}