fix(build): resolve Netlify deployment failures

- Add explicit Node.js runtime exports to 4 API routes
- Move TypeScript from dependencies to devDependencies (-9.1MB Lambda)
- Exclude TypeScript from Lambda bundle in next.config.ts
- Update @netlify/plugin-nextjs to v5.13.5

These changes resolve:
1. API routes defaulting to Edge runtime causing failures
2. TypeScript compiler bundled in Lambda (9.1MB waste)
3. Plugin version mismatch with Next.js 15.5.4

Expected impact:
- Lambda bundle size: 86MB → ~77MB (10% reduction)
- Proper runtime configuration for OpenAI/Stripe SDKs
- Improved build reliability

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

Author: apex-ai-net

app/api/create-checkout/route.ts

@@ -7,6 +7,9 @@ import { logger } from '@/lib/logger';
 import type { ConvexUserDoc } from '@/lib/supabase/convex-compat';
 import { getStripePriceId } from '@/lib/stripe/pricing-config';
 
+// Specify Node.js runtime (required for Stripe SDK and Supabase)
+export const runtime = 'nodejs';
+
 /**
  * Plan ID validation schema
  */

app/api/gpt5/documentation/route.ts

@@ -9,6 +9,9 @@ import { validateHealthcarePrompt } from "@/lib/prompts";
 import { docsRateLimiter, checkRateLimit } from "@/lib/rate-limit";
 import { logger } from "@/lib/logger";
 
+// Specify Node.js runtime (required for OpenAI SDK)
+export const runtime = 'nodejs';
+
 let cachedOpenAI: OpenAI | null = null;
 function getOpenAIClient(): OpenAI | null {
   const apiKey = process.env.OPENAI_API_KEY;

app/api/gpt5/function/route.ts

@@ -9,6 +9,9 @@ import { validateHealthcarePrompt } from "@/lib/prompts";
 import { fnRateLimiter, checkRateLimit } from "@/lib/rate-limit";
 import { logger } from "@/lib/logger";
 
+// Specify Node.js runtime (required for OpenAI SDK)
+export const runtime = 'nodejs';
+
 let cachedOpenAI: OpenAI | null = null;
 
 function getOpenAIClient(): OpenAI | null {

app/api/gpt5/route.ts

@@ -11,6 +11,9 @@ import { getUserTier, checkTieredRateLimit } from "@/lib/rate-limit";
 import { getSupabaseServerClient } from "@/lib/supabase/client";
 import { getCurrentStudent } from "@/lib/supabase/services/students";
 
+// Specify Node.js runtime (required for OpenAI SDK)
+export const runtime = 'nodejs';
+
 let cachedOpenAI: OpenAI | null = null;
 function getOpenAIClient(): OpenAI | null {
   const apiKey = process.env.OPENAI_API_KEY;

next.config.ts

@@ -168,6 +168,8 @@ const nextConfig: NextConfig = {
       'node_modules/webpack/**',
       'node_modules/terser/**',
       'node_modules/rollup/**',
+      // TypeScript compiler (build-time only, not needed in Lambda)
+      'node_modules/typescript/**',
       // Testing dependencies (not needed in production)
       'node_modules/playwright-core',
       'node_modules/@playwright',