test: setup Vitest workspace and Playwright with first nutrition tests

Vitest:
- Workspace at root (vitest.workspace.ts) running per-package configs
- packages/shared/vitest.config.ts with v8 coverage and 70% thresholds
- Root scripts: test / test:watch / test:coverage

Nutrition module in @ketopath/shared:
- calculateBmr (Mifflin-St Jeor) + calculateTdee with activity multipliers
- ACTIVITY_MULTIPLIERS constants matching CLAUDE.md domain knowledge
- 14 unit tests covering Michele/Laura PRD personas, all sex variants,
  every activity level, and input validation (100% coverage on src/nutrition)

Playwright in apps/web:
- chromium-only project, webServer auto-boot of pnpm dev
- e2e/home.spec.ts smoke test asserts Italian copy and disclaimer

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

packages/shared/src/nutrition/bmr.test.ts

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+import { describe, expect, it } from 'vitest';
+
+import { calculateBmr } from './bmr.js';
+
+describe('calculateBmr (Mifflin-St Jeor)', () => {
+  it('matches the male formula for the "Michele" PRD persona', () => {
+    // 49 anni, uomo, 76 kg, 170 cm
+    // 10·76 + 6.25·170 − 5·49 + 5 = 760 + 1062.5 − 245 + 5 = 1582.5
+    const bmr = calculateBmr({ weightKg: 76, heightCm: 170, ageYears: 49, gender: 'MALE' });
+    expect(bmr).toBeCloseTo(1582.5, 2);
+  });
+
+  it('matches the female formula for the "Laura" PRD persona', () => {
+    // 46 anni, donna, 70 kg, 165 cm
+    // 10·70 + 6.25·165 − 5·46 − 161 = 700 + 1031.25 − 230 − 161 = 1340.25
+    const bmr = calculateBmr({ weightKg: 70, heightCm: 165, ageYears: 46, gender: 'FEMALE' });
+    expect(bmr).toBeCloseTo(1340.25, 2);
+  });
+
+  it('uses the average sex-constant for OTHER', () => {
+    const male = calculateBmr({ weightKg: 70, heightCm: 170, ageYears: 30, gender: 'MALE' });
+    const female = calculateBmr({ weightKg: 70, heightCm: 170, ageYears: 30, gender: 'FEMALE' });
+    const other = calculateBmr({ weightKg: 70, heightCm: 170, ageYears: 30, gender: 'OTHER' });
+    expect(other).toBeCloseTo((male + female) / 2, 5);
+  });
+
+  it.each([
+    { weightKg: 0, heightCm: 170, ageYears: 30 },
+    { weightKg: 70, heightCm: 0, ageYears: 30 },
+    { weightKg: 70, heightCm: 170, ageYears: 0 },
+    { weightKg: -1, heightCm: 170, ageYears: 30 },
+  ])('rejects non-positive inputs %j', (input) => {
+    expect(() => calculateBmr({ ...input, gender: 'MALE' })).toThrow(RangeError);
+  });
+});

packages/shared/src/nutrition/bmr.ts

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+import type { Gender } from './types.js';
+
+export interface BmrInput {
+  weightKg: number;
+  heightCm: number;
+  ageYears: number;
+  gender: Gender;
+}
+
+// Mifflin-St Jeor equation. For Gender 'OTHER' we use the average of the
+// male and female sex-specific constants (-78), as a neutral approximation.
+export function calculateBmr({ weightKg, heightCm, ageYears, gender }: BmrInput): number {
+  if (weightKg <= 0 || heightCm <= 0 || ageYears <= 0) {
+    throw new RangeError('weightKg, heightCm and ageYears must be positive');
+  }
+
+  const base = 10 * weightKg + 6.25 * heightCm - 5 * ageYears;
+
+  switch (gender) {
+    case 'MALE':
+      return base + 5;
+    case 'FEMALE':
+      return base - 161;
+    case 'OTHER':
+      return base - 78;
+  }
+}

packages/shared/src/nutrition/tdee.test.ts

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+import { describe, expect, it } from 'vitest';
+
+import { calculateBmr } from './bmr.js';
+import { calculateTdee } from './tdee.js';
+
+describe('calculateTdee', () => {
+  it('multiplies BMR by sedentary factor 1.2 for "Michele"', () => {
+    const bmr = calculateBmr({ weightKg: 76, heightCm: 170, ageYears: 49, gender: 'MALE' });
+    expect(calculateTdee(bmr, 'SEDENTARY')).toBeCloseTo(1899, 1);
+  });
+
+  it('multiplies BMR by moderate factor 1.55 for "Laura"', () => {
+    const bmr = calculateBmr({ weightKg: 70, heightCm: 165, ageYears: 46, gender: 'FEMALE' });
+    expect(calculateTdee(bmr, 'MODERATE')).toBeCloseTo(2077.39, 2);
+  });
+
+  it.each([
+    ['SEDENTARY', 1.2],
+    ['LIGHT', 1.375],
+    ['MODERATE', 1.55],
+    ['INTENSE', 1.725],
+  ] as const)('applies the %s multiplier (%f)', (level, factor) => {
+    expect(calculateTdee(2000, level)).toBeCloseTo(2000 * factor, 5);
+  });
+
+  it('rejects non-positive BMR', () => {
+    expect(() => calculateTdee(0, 'SEDENTARY')).toThrow(RangeError);
+    expect(() => calculateTdee(-1, 'SEDENTARY')).toThrow(RangeError);
+  });
+});

packages/shared/src/nutrition/tdee.ts

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+import { ACTIVITY_MULTIPLIERS, type ActivityLevel } from './types.js';
+
+export function calculateTdee(bmr: number, activityLevel: ActivityLevel): number {
+  if (bmr <= 0) {
+    throw new RangeError('bmr must be positive');
+  }
+  return bmr * ACTIVITY_MULTIPLIERS[activityLevel];
+}

packages/shared/src/nutrition/types.ts

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+export type Gender = 'MALE' | 'FEMALE' | 'OTHER';
+
+export type ActivityLevel = 'SEDENTARY' | 'LIGHT' | 'MODERATE' | 'INTENSE';
+
+export const ACTIVITY_MULTIPLIERS: Record<ActivityLevel, number> = {
+  SEDENTARY: 1.2,
+  LIGHT: 1.375,
+  MODERATE: 1.55,
+  INTENSE: 1.725,
+};