try with 2 prerendering routes

.vercel/output/functions/api.func/.vc-config.json

@@ -1,4 +1,5 @@
 {
-  "runtime": "nodejs20.x",
-  "handler": "index.js"
-}
+  "runtime": "nodejs22.x",
+  "handler": "router.js",
+  "launcherType": "Nodejs"
+}

.vercel/output/functions/api.func/index.js

@@ -1,3 +0,0 @@
-export default async (req, res) => {
-    return res.send("hello world");
-};

.vercel/output/functions/api.func/package.json

@@ -0,0 +1,3 @@
+{
+  "type": "module"
+}

.vercel/output/functions/api.func/router.js

@@ -0,0 +1,19 @@
+import { default as gist } from './core-app/api/gist.js'
+import { default as pin } from './core-app/api/pin.js'
+
+export default async (req, res) => {
+    const url = new URL(req.url, 'https://localhost')
+    req.query = Object.fromEntries(url.searchParams.entries())
+    switch(url.pathname) {
+        case '/gist':
+            gist(req, res)
+            break
+        case '/pin':
+            pin(req, res)
+            break
+        default:
+            res.statusCode = 404
+            res.end('Not Found')
+            break
+    }
+}

.vercel/output/functions/api.prerender-config.json

@@ -1,3 +1,5 @@
 {
-  "expiration": 5
+  "expiration": 5,
+  "bypassToken": "r3fr3shT0k3n",
+  "passQuery": true
 }

.vercel/output/functions/gist.func

@@ -0,0 +1 @@
+api.func

.vercel/output/functions/gist.prerender-config.json

@@ -0,0 +1,5 @@
+{
+  "expiration": 5,
+  "bypassToken": "r3fr3shT0k3n",
+  "passQuery": true
+}

.vercel/output/functions/pin.func

@@ -0,0 +1 @@
+api.func

.vercel/output/functions/pin.prerender-config.json

@@ -0,0 +1,5 @@
+{
+  "expiration": 5,
+  "bypassToken": "r3fr3shT0k3n",
+  "passQuery": true
+}