Define an Inngest function and serve it from a Next.js App Router route handler

Documented steps

1. Create the client in `src/inngest/client.ts`: `import { Inngest } from "inngest"; export const inngest = new Inngest({ id: "my-app" });`
2. Define a function with the current two-argument form — the trigger lives INSIDE the first config object: `inngest.createFunction({ id: "import-product-images", triggers: { event: "shop/product.imported" } }, async ({ event, step, runId }) => { /* ... */ });`. Ref: https://www.inngest.com/docs/reference/functions/create
3. Create the serve endpoint at `src/app/api/inngest/route.ts`: `import { serve } from "inngest/next"; import { inngest } from "../../../inngest/client"; import fnA from "../../../inngest/fnA"; export const { GET, POST, PUT } = serve({ client: inngest, functions: [fnA] });`
4. Export all three of GET, POST and PUT. GET serves introspection, POST executes function steps, PUT performs registration/sync. Ref: https://www.inngest.com/docs/learn/serving-inngest-functions
5. Set `INNGEST_SIGNING_KEY` in the hosting environment (or pass `signingKey` to the Inngest client constructor). It authenticates SDK↔Inngest traffic and determines which Inngest environment the app syncs into.
6. Run `npx inngest-cli@latest dev -u http://localhost:3000/api/inngest` and confirm the function appears in the Dev Server UI at http://localhost:8288.
7. For production, sync the app: dashboard → Apps → Sync App with the serve URL, use the Vercel/Netlify integration for auto-sync on deploy, or POST `https://api.inngest.com/v2/apps/$APP_ID/syncs` with `Authorization: Bearer $INNGEST_API_KEY` and body `{"url":"$APP_URL"}`. Ref: https://www.inngest.com/docs/apps/cloud