Add Prettier for code formatting

[finnar-bin]

Resolves #127

Summary

• Adds Prettier as a devDependency using its default configuration only — no .prettierrc is included. This is intentional: the issue calls for matching manager-ui's zero-decision setup, so there's no repo-specific config to diverge from.
• Adds format / format:check npm scripts and a .prettierignore scoped to src/**/*.{ts,tsx}.
• Adds a husky + pretty-quick --staged pre-commit hook so new commits auto-format and can't drift out of style again. The prepare script is husky || true (not plain husky) — this is husky's own documented pattern so that npm ci --omit=dev (production/CI installs without devDependencies) doesn't fail with "husky: not found".
• One-time mechanical reformat of 47 files under src/ via npx prettier --write "src/**/*.{ts,tsx}" — no logic changes. This is deliberately its own commit (ecad319), separate from the tooling commit (99ccfd9) that adds Prettier itself, so the reformat diff doesn't get tangled up with the tooling/config changes during review (this was itself an acceptance criterion on the issue).
• Updates CLAUDE.md to document the new formatting tooling.

Out of scope

• CI wiring — format:check is not wired into any CI workflow here. That's intentionally deferred to a separate issue covering the CI build/typecheck gate.
• ESLint — no ESLint rules were added or changed for formatting concerns; Prettier owns formatting only.

Test plan

• npm run format:check exits clean on this branch
• npx tsc --noEmit passes clean (confirms the mechanical reformat introduced no type errors)
• Stage an intentionally unformatted file and confirm the pre-commit hook (husky + pretty-quick) auto-formats it before commit
• npm ci --omit=dev does not fail on the prepare script (husky guard)

Notes

Pure formatting + build-tooling change — no visual or runtime behavior change, so no screenshots are included.

[github-actions]

Code Review — ✅ No blockers