Managed Functions deployment consistently fails with "Failed to deploy the Azure Functions" on Free tier — reproducible with zero-dependency function

## Summary
Every attempt to deploy an API (managed Azure Functions, via `swa deploy --api-location`) to a Free-tier Static Web App fails with the generic "Failed to deploy the Azure Functions" reason, after a consistent ~16 second delay. Frontend-only deployment (no `--api-location`) succeeds without issue on the same resource.

## Environment
- Static Web App SKU: Free
- Region: East US 2 (also tried West Europe / North Europe, both rejected at creation time with "region not accepting new customers" — unrelated to this issue)
- SWA CLI version: 2.0.10
- Node.js API, `apiVersion: 22` (also tried with explicit `"platform": {"apiRuntime": "node:22"}` in staticwebapp.config.json — no change)
- Deployment method: `swa deploy` with a deployment token (not GitHub Actions)
- OS: Windows 11

## Steps to reproduce
1. Create a Free-tier Static Web App via `az staticwebapp create`.
2. Create a minimal API with a single HTTP-triggered function, zero dependencies beyond `@azure/functions`.
3. Build it (`tsc`), producing a clean `dist/` with one compiled function file and `host.json` at the API root.
4. Deploy: `swa deploy ./dist --api-location ./api --deployment-token --env production`

## Expected
The single trivial function deploys successfully.

## Actual
Deployment fails every time, identically:

## Troubleshooting already done
- Confirmed not a stale-build-artifact issue (clean `dist/`, verified exact file list before zipping).
- Confirmed not a bloated/dev-dependency issue (`npm prune --omit=dev` before deploy).
- Confirmed not a runtime-version issue (Node 22 is on the documented supported list; explicit `apiRuntime` config made no difference).
- Confirmed not specific to one resource instance: fully deleted and recreated the Static Web App, identical failure on the fresh resource.
- Confirmed not specific to our actual application code: deployed a single-endpoint function with zero dependencies beyond `@azure/functions`, identical failure.
- Frontend-only deployment (same resource, `swa deploy ./dist` without `--api-location`) succeeds cleanly every time.
- Azure Portal's Activity Log shows no entry corresponding to this failure (deployment appears to go through a non-ARM data-plane path not captured there).
- Azure Portal's "Diagnose and solve problems" tool for the resource did not surface anything more specific.

This strongly suggests either a platform-side issue specific to this subscription/tier combination, or an undocumented restriction on managed Functions for Free-tier Static Web Apps that isn't reflected in current error messaging.

Start by reproducing the failure with the zero-dependency Node.js function, the `swa deploy` command, and the Free-tier Static Web App described here. Check the `--api-location` deployment path and the `staticwebapp.config.json` and `host.json` inputs, then compare with frontend-only deployment. Done means identifying the platform or CLI cause and making managed Functions deployment succeed, or producing a specific actionable error.

Written by the indexing model from the issue text.