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/model.go

@@ -13,7 +13,7 @@ type User struct {
 	AvatarURL     *string         `json:"avatar_url"`
 	HeightCM      *int            `json:"height_cm"`
 	WeightKG      *float64        `json:"weight_kg"`
-	Age           *int            `json:"age"`
+	DateOfBirth   *string         `json:"date_of_birth"`
 	Gender        *string         `json:"gender"`
 	Activity      *string         `json:"activity"`
 	Goal          *string         `json:"goal"`
@@ -28,7 +28,7 @@ type UpdateProfileRequest struct {
 	Name          *string          `json:"name"`
 	HeightCM      *int             `json:"height_cm"`
 	WeightKG      *float64         `json:"weight_kg"`
-	Age           *int             `json:"age"`
+	DateOfBirth   *string          `json:"date_of_birth"`
 	Gender        *string          `json:"gender"`
 	Activity      *string          `json:"activity"`
 	Goal          *string          `json:"goal"`
@@ -39,6 +39,6 @@ type UpdateProfileRequest struct {
 // HasBodyParams returns true if any body parameter is being updated
 // that would require recalculation of daily calories.
 func (r *UpdateProfileRequest) HasBodyParams() bool {
-	return r.HeightCM != nil || r.WeightKG != nil || r.Age != nil ||
+	return r.HeightCM != nil || r.WeightKG != nil || r.DateOfBirth != nil ||
 		r.Gender != nil || r.Activity != nil || r.Goal != nil
 }