App Router + Pages Router API endpoints: `pages/api/*` unreachable from app-dir suite

This issue was created by an agent analysing CI failures from the Next.js Deploy Suite (vinext main vs Next.js v16.2.6, 2026-05-22).

Problem

When an App Router app coexists with Pages Router pages/api/* endpoints (e.g., /api/dump-headers-serverless, /api/dump-headers-edge), vinext serves an HTML This page could not be found page instead of executing the API route. This breaks middleware-driven request-header inspection tests for both serverless and edge runtimes and also breaks draft-mode flows that rely on the Pages API endpoint.

FetchError: invalid json response body at .../api/dump-headers-serverless reason: Unexpected token 'T', "This page "...

FetchError: invalid json response body at .../api/dump-headers-edge

Estimated Impact

~8 test failures across the deploy suite.

Affected Test Suites

• test/e2e/app-dir/app-middleware/app-middleware.test.ts (8 failures)

Recommendation

1. Reproduce first in vinext's own test suite. Add a fixture with both app/ and pages/api/* and assert the API routes return JSON.

2. Make the router dispatch fall through to pages/api/*. When the App Router does not match a request, the dispatcher must try Pages Router API routes before serving the not-found page.

3. Cover the draft-mode test paths. The same fix should restore the draft-mode flow that POSTs to the Pages API endpoint.

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Part of #1328.