docs: improve developer setup guide

[beanscg]

Fixes #16.

This makes the developer setup path more complete and easier to verify for new contributors.

Changes:

• Correct the clone URL and local directory name to match this repository.
• Add Node/npm/Git prerequisites.
• Document the local development, lint, build, and production-start commands.
• Add a short architecture overview for the Next.js app structure.
• Expand the pull-request checklist in CONTRIBUTING.md to include lint/build validation and manual test notes.

Validation:

• npm install completed.
• npm run build passed.
• Direct content check confirmed the updated setup commands and architecture overview.
• git diff --check

Note: npm run lint was attempted and failed on existing source issues unrelated to this docs change:

• src/types/keyboard.ts: @typescript-eslint/no-explicit-any
• unused variable warnings in src/app/page.tsx and src/components/KeycodePicker.tsx

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