feat: custom JWT auth + i18n with Chinese default

Replace Clerk with self-contained JWT auth (bcryptjs + jose), remove all
external auth dependencies. Add full i18n system with Chinese as default
language and English toggle — React Context + JSON dictionaries, no
external i18n library.

Auth:
- Add passwordHash to User model, generate JWT secret
- Create /api/auth/register, login, logout, me endpoints
- Rewrite proxy.ts middleware for custom session validation
- Add AuthProvider + useAuth hook, sign-in/sign-up pages
- Wire auth into layout and all API routes

i18n:
- React Context I18nProvider with localStorage + cookie persistence
- dictionaries/zh.ts (default) and dictionaries/en.ts
- LanguageSwitcher component, server-side createServerT() utility
- CJK font stack via [lang="zh"] CSS selector
- HTML lang attribute synced on language change
- All pages, components, TabBar, StageBadge translated
- Engine fallback strings (reflection-analyzer, summary-generator)
- API routes pass locale from cookie to engines

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

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

@@ -1,10 +1,11 @@
-import { auth } from "@clerk/nextjs/server";
+import { getSession } from "@/lib/auth";
 import { NextResponse } from "next/server";
 import { prisma } from "@/lib/prisma";
 
 export async function GET() {
-  const { userId } = await auth();
-  if (!userId) return NextResponse.json({ error: "Unauthorized" }, { status: 401 });
+  const session = await getSession();
+  if (!session) return NextResponse.json({ error: "Unauthorized" }, { status: 401 });
+  const userId = session.userId;
 
   const state = await prisma.userState.findUnique({
     where: { userId },
@@ -35,8 +36,9 @@ export async function GET() {
 }
 
 export async function PATCH(req: Request) {
-  const { userId } = await auth();
-  if (!userId) return NextResponse.json({ error: "Unauthorized" }, { status: 401 });
+  const session = await getSession();
+  if (!session) return NextResponse.json({ error: "Unauthorized" }, { status: 401 });
+  const userId = session.userId;
 
   const body = await req.json().catch(() => null);
   if (!body || typeof body !== "object") {