Scaffold Vercel serverless serving for Elysia backend

Add a second tsdown entry (src/server/vercel.ts -> dist/vercel.mjs, no-listen handler bundle), a thin api/index.ts Vercel function that re-exports it, and a vercel.json rewrite routing all paths to the function. Needs real-deploy verification (native-dep tracing, rewrite path preservation).

apps/backend/api/index.ts

@@ -0,0 +1,21 @@
+// Vercel serverless entry for the Elysia backend.
+//
+// We do NOT bundle the whole backend graph here (the `@/*` and `next/*` alias
+// resolution + heavy native deps are handled by tsdown). Instead this thin
+// function re-exports the already-built handler bundle (`dist/vercel.mjs`,
+// produced by `tsdown` during `turbo build`), and Vercel's function builder
+// only has to trace the externalized native deps (prisma, sharp, bcrypt,
+// oidc-provider, pg) from node_modules.
+//
+// All requests are routed here via the `rewrites` rule in vercel.json, so the
+// Elysia app does its own routing/version-rewrite against the original URL.
+import app from "../dist/vercel.mjs";
+
+export const config = {
+  runtime: "nodejs",
+  maxDuration: 60,
+};
+
+export default function handler(request: Request): Response | Promise<Response> {
+  return app.handle(request);
+}

apps/backend/tsdown.config.ts

@@ -87,7 +87,10 @@ const plugins = [
 ];
 
 export default defineConfig({
-  entry: [resolve(backendDir, "src/server/server.ts")],
+  entry: [
+    resolve(backendDir, "src/server/server.ts"),
+    resolve(backendDir, "src/server/vercel.ts"),
+  ],
   format: ["esm"],
   outDir: resolve(backendDir, "dist"),
   target: "node22",

apps/backend/vercel.json

@@ -1,6 +1,9 @@
 {
   "$schema": "https://openapi.vercel.sh/vercel.json",
   "framework": null,
+  "rewrites": [
+    { "source": "/(.*)", "destination": "/api" }
+  ],
   "crons": [
     {
       "path": "/api/latest/internal/email-queue-step",