feat(profile): persist and expose the date-format preference

Accept dateFormat on the profile PATCH field-by-field, echo it from
the profile + /me reads, mirror it into the client auth user, and add
the field to the OpenAPI request/response schemas.

src/app/api/auth/me/route.ts

@@ -96,6 +96,10 @@ export const GET = apiHandler(async () => {
     // Hour-cycle display preference (AUTO follows the locale convention,
     // H12 / H24 pin the cycle). Clients mirror this into their formatters.
     timeFormat: user.timeFormat ?? "AUTO",
+    // Date-order display preference (AUTO follows the locale convention,
+    // DMY / MDY / YMD pin the field order). Clients mirror this into their
+    // formatters and the <DateField> primitive.
+    dateFormat: user.dateFormat ?? "AUTO",
     lastReportPracticeName: user.lastReportPracticeName ?? null,
     // v1.4.47 W3 — per-user Coach opt-out. Default `false` if the
     // column is absent (partial-deploy rollback safety, see migration

src/app/api/user/profile/route.ts

@@ -42,6 +42,7 @@ export const GET = apiHandler(async () => {
         locale: true,
         timezone: true,
         timeFormat: true,
+        dateFormat: true,
         moodReminderEnabled: true,
         fullName: true,
         insurerName: true,
@@ -77,6 +78,7 @@ export const GET = apiHandler(async () => {
     locale: dbUser?.locale ?? null,
     timezone: dbUser?.timezone ?? "Europe/Berlin",
     timeFormat: dbUser?.timeFormat ?? "AUTO",
+    dateFormat: dbUser?.dateFormat ?? "AUTO",
     moodReminderEnabled: dbUser?.moodReminderEnabled ?? false,
     fullName: dbUser?.fullName ?? null,
     insurerName: dbUser?.insurerName ?? null,
@@ -114,6 +116,7 @@ export const PATCH = apiHandler(async (request: NextRequest) => {
     locale: result.user.locale,
     timezone: result.user.timezone,
     timeFormat: result.user.timeFormat,
+    dateFormat: result.user.dateFormat,
     moodReminderEnabled: result.user.moodReminderEnabled,
     fullName: result.user.fullName,
     insurerName: result.user.insurerName,