fix: auth login flow, Next.js 16 upgrade, ESM/CJS compatibility

- Upgrade Next.js 15 → 16.1 and rename middleware.ts → proxy.ts
- Fix ESM/CJS compatibility: remove "type": "module" from config/shared packages, switch to commonjs
- Fix Better Auth integration: text IDs for sessions/accounts/verifications, wildcard route @All("**"), proper password hash for admin seed
- Fix auth-client to use window.location.origin instead of hardcoded localhost:4000
- Fix api-client, forgot-password, reset-password to use relative /api/ URLs (via Next.js proxy)
- Fix TimeoutInterceptor DI by using useValue instead of useClass
- Add Playwright E2E login tests for localhost and v2.sase.tr
- Add missing UI components: vin-input, vehicle-card, category-tree

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

apps/web/src/lib/api-client.ts

@@ -1,4 +1,4 @@
-const API_URL = process.env.NEXT_PUBLIC_API_URL || "http://localhost:4000/api";
+const API_URL = "/api";
 
 type RequestOptions = {
   method?: string;

apps/web/src/lib/auth-client.ts

@@ -1,7 +1,7 @@
 import { createAuthClient } from "better-auth/react";
 
 export const authClient = createAuthClient({
-  baseURL: process.env.NEXT_PUBLIC_API_URL?.replace("/api", "") || "http://localhost:4000",
+  baseURL: typeof window !== "undefined" ? window.location.origin : (process.env.NEXT_PUBLIC_APP_URL || "http://localhost:3000"),
   basePath: "/api/auth",
 });