Don't return a Response in inngest/next if in serverless (#421)

## Summary
<!-- Succinctly describe your change, providing context, what you've
changed, and why. -->

Next.js versions `next@>=13.0.0 <13.5.0` will throw an error if a
`Response` object is returned from a serverless endpoint.
`next@>=13.5.0` will display the error but continue to function.

Next.js edge still requires that the `ReturnType` of the function is a
`Response`, so we keep that type whilst ensuring it's not actually
passed back in serverless endpoints.

There are so many edge cases here and this one breaks across minor
versions. Separate exports (e.g. `inngest/next-13-edge`) might be
appropriate in the future if the type/runtime guards continue to become
stricter on the Next.js side.

## Checklist
<!-- Tick these items off as you progress. -->
<!-- If an item isn't applicable, ideally please strikeout the item by
wrapping it in "~~"" and suffix it with "N/A My reason for skipping
this." -->
<!-- e.g. "- [ ] ~~Added tests~~ N/A Only touches docs" -->

- [ ] ~~Added a [docs PR](https://github.com/inngest/website) that
references this PR~~ N/A Bug fix
- [ ] ~~Added unit/integration tests~~ N/A Will observe logs
disappearing in current integration tests which use `[email protected]`:
https://github.com/inngest/inngest-js/actions/runs/7181668471/job/19556571083?pr=421
- [x] Added changesets if applicable

## Related
<!-- A space for any related links, issues, or PRs. -->
<!-- Linear issues are autolinked. -->
<!-- e.g. - INN-123 -->
<!-- GitHub issues/PRs can be linked using shorthand. -->
<!-- e.g. "- inngest/inngest#123" -->
<!-- Feel free to remove this section if there are no applicable related
links.-->
- #400

.changeset/silly-dolphins-pump.md

@@ -0,0 +1,5 @@
+---
+"inngest": patch
+---
+
+Fix serverless use of `inngest/next` with `next@>=13.0.0 <13.5.0` failing to return a response, as well as `next@>=13.5.0` logging the same error

packages/inngest/src/next.ts

@@ -14,6 +14,8 @@ export const frameworkName: SupportedFrameworkName = "nextjs";
  * In Next.js, serve and register any declared functions with Inngest, making
  * them available to be triggered by events.
  *
+ * Supports Next.js 12+, both serverless and edge.
+ *
  * @example Next.js <=12 or the pages router can export the handler directly
  * ```ts
  * export default serve({ client: inngest, functions: [fn1, fn2] });
@@ -150,15 +152,21 @@ export const serve = (options: ServeHandlerOptions) => {
             typeof res?.send === "function"
           ) {
             res.status(status).send(body);
+
+            /**
+             * If we're here, we're in a serverless endpoint (not edge), so
+             * we've correctly sent the response and can return `undefined`.
+             *
+             * Next.js 13 edge requires that the return value is typed as
+             * `Response`, so we still enforce that as we cannot dynamically
+             * adjust typing based on the environment.
+             */
+            return undefined as unknown as Response;
           }
 
           /**
-           * Next.js 13 requires that the return value is always `Response`,
-           * though this serve handler can't understand if we're using 12 or 13.
-           *
-           * 12 doesn't seem to care if we also return a response from the
-           * handler, so we'll just return `undefined` here, which will be safe
-           * at runtime and enforce types for use with Next.js 13.
+           * If we're here, we're in an edge environment and need to return a
+           * `Response` object.
            *
            * We also don't know if the current environment has a native
            * `Response` object, so we'll grab that first.