fix: call instrumentationHook earlier for prod server (#63536)

This ensures that the instrumentation hook for Node.js will run
immediately during `next start` instead of waiting for the first request
like does it `next dev`.

However, if there is a separate instrumentation hook for Edge, that will
still be lazy evaluated and wait until the first request.

Fixes #59999 
Fixes NEXT-2738

packages/next/src/server/next-server.ts

@@ -252,6 +252,16 @@ export default class NextNodeServer extends BaseServer {
     }
 
     this.middlewareManifestPath = join(this.serverDistDir, MIDDLEWARE_MANIFEST)
+
+    // This is just optimization to fire prepare as soon as possible. It will be
+    // properly awaited later. We add the catch here to ensure that it does not
+    // cause a unhandled promise rejection. The promise rejection will be
+    // handled later on via the `await` when the request handler is called.
+    if (!options.dev) {
+      this.prepare().catch((err) => {
+        console.error('Failed to prepare server', err)
+      })
+    }
   }
 
   protected async handleUpgrade(): Promise<void> {

test/e2e/instrumentation-hook/instrumentation-hook.test.ts

@@ -67,14 +67,12 @@ describe('Instrumentation Hook', () => {
 
   describeCase('with-node-api', ({ next }) => {
     it('with-node-api should run the instrumentation hook', async () => {
-      await next.render('/api')
       await check(() => next.cliOutput, /instrumentation hook on nodejs/)
     })
   })
 
   describeCase('with-node-page', ({ next }) => {
     it('with-node-page should run the instrumentation hook', async () => {
-      await next.render('/')
       await check(() => next.cliOutput, /instrumentation hook on nodejs/)
     })
   })