feat: replace age integer with date_of_birth across backend and client

Store date_of_birth (DATE) instead of a static age integer so that age
is always computed dynamically from the stored date of birth.

- Migration 011: adds date_of_birth, backfills from age, drops age
- AgeFromDOB helper computes current age from YYYY-MM-DD string
- User model, repository SQL, and service validation updated
- Flutter: User.age becomes a computed getter; profile edit screen
  uses a date picker bounded to [today-120y, today-10y]

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/internal/user/calories.go

@@ -1,6 +1,9 @@
 package user
 
-import "math"
+import (
+	"math"
+	"time"
+)
 
 // Activity level multipliers (Mifflin-St Jeor).
 var activityMultiplier = map[string]float64{
@@ -16,6 +19,23 @@ var goalAdjustment = map[string]float64{
 	"gain":     300,
 }
 
+// AgeFromDOB computes age in years from a "YYYY-MM-DD" string. Returns nil on error.
+func AgeFromDOB(dob *string) *int {
+	if dob == nil {
+		return nil
+	}
+	t, err := time.Parse("2006-01-02", *dob)
+	if err != nil {
+		return nil
+	}
+	now := time.Now()
+	years := now.Year() - t.Year()
+	if now.Month() < t.Month() || (now.Month() == t.Month() && now.Day() < t.Day()) {
+		years--
+	}
+	return &years
+}
+
 // CalculateDailyCalories computes the daily calorie target using the
 // Mifflin-St Jeor equation. Returns nil if any required parameter is missing.
 func CalculateDailyCalories(heightCM *int, weightKG *float64, age *int, gender, activity, goal *string) *int {