chore: package.json hygiene — missing format/typecheck scripts, shadcn CLI in prod dependencies

[shauryagangrade]

Problem

Small but real papercuts in package.json:

1. No format script — Prettier isn't configured at all, so formatting is ad hoc across files
2. No typecheck script — CI hardcodes npx tsc --noEmit, so local contributors can't run the same gate easily (npm run typecheck)
3. No test:watch
4. shadcn (a CLI) sits in production dependencies — should be devDependencies (or dropped for npx shadcn@latest)
5. eslint-config-next pinned 16.2.7 while next is ^16.2.9

Acceptance criteria

• npm run format / format:check / typecheck exist and CI uses them
• shadcn moved out of runtime deps