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/lib/engines/summary-generator.ts

@@ -1,6 +1,12 @@
 import OpenAI from "openai";
 import { prisma } from "@/lib/prisma";
 import { keywordCheck, llmSafetyCheck, type SafetyResult } from "@/lib/safety";
+import type { Lang } from "@/lib/i18n/types";
+import { createServerT } from "@/lib/i18n/utils";
+import zh from "../../../dictionaries/zh";
+import en from "../../../dictionaries/en";
+
+const DICTS = { zh, en } as const;
 
 // ---------------------------------------------------------------------------
 // Types
@@ -56,8 +62,11 @@ Voice rules:
 
 export async function generateWeeklySummary(
   userId: string,
-  openai: OpenAI
+  openai: OpenAI,
+  locale: Lang = "zh"
 ): Promise<GeneratedSummary> {
+  const t = createServerT(DICTS[locale]);
+
   // Gather week data
   const weekAgo = new Date();
   weekAgo.setDate(weekAgo.getDate() - 7);
@@ -85,8 +94,7 @@ export async function generateWeeklySummary(
 
   if (!userState || sessions.length === 0) {
     return {
-      summary:
-        "No completed practice sessions this week. Every week is a fresh start — your practice is here when you're ready.",
+      summary: t("engine.summary.no_sessions"),
       safety: { safe: true },
     };
   }
@@ -124,7 +132,7 @@ export async function generateWeeklySummary(
     // Safety check
     const keywordResult = keywordCheck(summary);
     if (!keywordResult.safe) {
-      return { summary: "Your practice summary for this week.", safety: keywordResult };
+      return { summary: t("engine.summary.safety_fallback"), safety: keywordResult };
     }
 
     const llmSafety = await llmSafetyCheck(summary, openai as any);
@@ -133,25 +141,34 @@ export async function generateWeeklySummary(
     const weekStart = new Date(weekAgo);
     weekStart.setHours(0, 0, 0, 0);
 
+    const safetyFallback = t("engine.summary.safety_fallback");
+
     await prisma.weeklySummary.upsert({
       where: { userId },
       create: {
         userId,
-        summary: llmSafety.safe ? summary : "Your practice summary for this week.",
+        summary: llmSafety.safe ? summary : safetyFallback,
         weekStart,
       },
       update: {
-        summary: llmSafety.safe ? summary : "Your practice summary for this week.",
+        summary: llmSafety.safe ? summary : safetyFallback,
         weekStart,
       },
     });
 
     return {
-      summary: llmSafety.safe ? summary : "Your practice summary for this week.",
+      summary: llmSafety.safe ? summary : safetyFallback,
       safety: llmSafety,
     };
   } catch {
-    const fallback = `You completed ${sessions.length} practice session${sessions.length === 1 ? "" : "s"} this week. Showing up consistently is the foundation everything else is built on. Your current streak is ${userState.streakDays} day${userState.streakDays === 1 ? "" : "s"}. See you next week.`;
+    const count = sessions.length;
+    const streak = userState.streakDays;
+    const fallback = t("engine.summary.fallback_template", {
+      count,
+      plural: count === 1 ? "" : "s",
+      streak,
+      streak_plural: streak === 1 ? "" : "s",
+    });
     return { summary: fallback, safety: { safe: true } };
   }
 }
@@ -161,7 +178,8 @@ export async function generateWeeklySummary(
 // ---------------------------------------------------------------------------
 
 export async function generateAllWeeklySummaries(
-  openai: OpenAI
+  openai: OpenAI,
+  locale: Lang = "zh"
 ): Promise<{ userId: string; success: boolean }[]> {
   // Find users who had sessions in the last 7 days
   const weekAgo = new Date();
@@ -180,7 +198,7 @@ export async function generateAllWeeklySummaries(
 
   for (const { userId } of activeUsers) {
     try {
-      await generateWeeklySummary(userId, openai);
+      await generateWeeklySummary(userId, openai, locale);
       results.push({ userId, success: true });
     } catch {
       results.push({ userId, success: false });