fix(account): answer profile writes with the derived birth-time truth

A zero-uncertainty exact declaration is accepted server-side as the active
minute, but the account write only answered {ok:true}. Every save path then
kept the draft it submitted, so the first consultation after initialization
asked for unverified_birth_time against an accepted profile and was rejected
with mode_changed before billing.

The account route now returns the status and active minute it derived, and
every profile save adopts that result instead of its own local guess.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/app/api/account/route.ts

@@ -6,6 +6,7 @@ import {
   accountProfilePatchSchema,
   applyAccountProfileConcurrencyGuards,
   resolveAccountBirthTimeApplicationPatch,
+  resolveAppliedAccountBirthTime,
 } from "@/lib/account-profile-patch";
 import { optionalBeamAvatarFromProfile } from "@/lib/beam-avatar";
 import { createAdminSupabaseClient, isAdminUser } from "@/lib/supabase/admin";
@@ -271,7 +272,10 @@ export async function PATCH(request: Request) {
       return NextResponse.json({ error: "暂时无法保存账户资料" }, { status: 500 });
     }
 
-    return NextResponse.json({ ok: true });
+    return NextResponse.json({
+      ok: true,
+      birthTime: resolveAppliedAccountBirthTime(currentProfile, applicationPatch),
+    });
   } catch (error) {
     if (isSupabaseConfigurationError(error)) {
       return NextResponse.json({ error: "Supabase 尚未配置", code: "SUPABASE_NOT_CONFIGURED" }, { status: 503 });