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/service.go

@@ -3,6 +3,7 @@ package user
 import (
 	"context"
 	"fmt"
+	"time"
 )
 
 type Service struct {
@@ -46,10 +47,11 @@ func (s *Service) UpdateProfile(ctx context.Context, userID string, req UpdatePr
 	if req.WeightKG != nil {
 		weight = req.WeightKG
 	}
-	age := current.Age
-	if req.Age != nil {
-		age = req.Age
+	dob := current.DateOfBirth
+	if req.DateOfBirth != nil {
+		dob = req.DateOfBirth
 	}
+	age := AgeFromDOB(dob)
 	gender := current.Gender
 	if req.Gender != nil {
 		gender = req.Gender
@@ -89,9 +91,17 @@ func validateProfileRequest(req UpdateProfileRequest) error {
 			return fmt.Errorf("weight_kg must be between 30 and 300")
 		}
 	}
-	if req.Age != nil {
-		if *req.Age < 10 || *req.Age > 120 {
-			return fmt.Errorf("age must be between 10 and 120")
+	if req.DateOfBirth != nil {
+		t, err := time.Parse("2006-01-02", *req.DateOfBirth)
+		if err != nil {
+			return fmt.Errorf("date_of_birth must be in YYYY-MM-DD format")
+		}
+		if t.After(time.Now()) {
+			return fmt.Errorf("date_of_birth cannot be in the future")
+		}
+		age := AgeFromDOB(req.DateOfBirth)
+		if *age < 10 || *age > 120 {
+			return fmt.Errorf("date_of_birth must yield an age between 10 and 120")
 		}
 	}
 	if req.Gender != nil {