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:
```
i Status: InProgress. Time: 0.66(s)
i Status: Failed. Time: 16.24(s)
i Deployment Failed :(
i Deployment Failure Reason: Failed to deploy the Azure Functions.
```

## 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.

No repository file or test entry point is named. Start by reproducing the documented `swa deploy ./dist --api-location ./api` case on a Free-tier Static Web App, then compare it with the successful frontend-only deployment. Done means the failure is explained with a reproducible resolution or a documented Free-tier restriction and clearer error handling.

Written by the indexing model from the issue text.