Feature Request: Support for AI Gateway Authenticated Gateway (cf-aig-authorization header)

## Summary

Moltworker currently does not support Cloudflare AI Gateway's [Authenticated Gateway](https://developers.cloudflare.com/ai-gateway/configuration/authentication/) feature. When Authenticated Gateway is enabled on the AI Gateway, all requests from Moltworker fail because the required `cf-aig-authorization` header is never sent.

## Problem

Cloudflare recommends enabling Authenticated Gateway when storing logs (which is the whole point of using AI Gateway for analytics/cost tracking). However, when enabled, every request to the gateway must include a `cf-aig-authorization` header containing a valid API token.

The Moltworker architecture makes this impossible because:

1. **The moltbot binary inside the container makes the API calls, not the Worker.** In `src/gateway/env.ts`, the Worker maps `AI_GATEWAY_BASE_URL` → `ANTHROPIC_BASE_URL` and `AI_GATEWAY_API_KEY` → `ANTHROPIC_API_KEY` as environment variables passed to the container. The moltbot binary then makes standard HTTP requests using only `x-api-key` — it has no mechanism to include `cf-aig-authorization`.

2. **No AI Gateway binding in `wrangler.jsonc`.** Cloudflare docs note: *"When an AI Gateway is accessed from a Cloudflare Worker using a binding, the `cf-aig-authorization` header does not need to be manually included."* However, Moltworker uses URL-based access from inside the container, not Worker bindings. Even if a binding were added to the Worker, it can't be passed into the container — the container only receives environment variables (strings).

3. **No env var or config option exists** to pass an additional authentication token/header for the gateway.

## Steps to Reproduce

1. Deploy Moltworker with AI Gateway configured (`AI_GATEWAY_BASE_URL` + `AI_GATEWAY_API_KEY`)
2. Enable "Authenticated Gateway" in AI Gateway Settings
3. Send a message through the Control UI
4. Observe: AI Gateway logs show the request is rejected (no `cf-aig-authorization` header present)

## Current Workaround

Disable Authenticated Gateway in the AI Gateway settings. This works but means the gateway endpoint is unauthenticated — anyone who discovers the gateway URL could route requests through it.

## Proposed Solutions

### Option A: Proxy API calls through the Worker (recommended)

Instead of having the container call the AI Gateway URL directly, have the Worker act as a proxy:
- Container sends API requests to the Worker (e.g., `http://localhost:{port}/api/proxy`)
- The Worker intercepts and forwards them to AI Gateway using a [Worker AI Gateway binding](https://developers.cloudflare.com/ai-gateway/providers/workersai/#worker-binding), which auto-includes the `cf-aig-authorization` header
- This would also enable future use of AI Gateway features that require Worker bindings

### Option B: Pass `cf-aig-authorization` as an env var

Add a new secret (e.g., `AI_GATEWAY_AUTH_TOKEN`) that gets passed to the container. The moltbot binary would need to be updated to include this as a `cf-aig-authorization` header on requests to the gateway URL.

### Option C: Add `ai` binding to `wrangler.jsonc`

Configure an AI Gateway binding in the wrangler config and have the Worker make the AI API calls on behalf of the container, using the binding which auto-authenticates.

## Environment

- Moltworker commit: `7b0ba7811b7558fdc158cb53cd0a0e4327e9a429` (main, Jan 30 2026)
- Relevant files: `src/gateway/env.ts`, `src/types.ts`, `wrangler.jsonc`

## References

- [Cloudflare AI Gateway Authenticated Gateway docs](https://developers.cloudflare.com/ai-gateway/configuration/authentication/)
- [Blog post: Introducing Moltworker](https://blog.cloudflare.com/moltworker-self-hosted-ai-agent/) — mentions AI Gateway but not Authenticated Gateway

cc @brianbrunner @sidharthachatterjee @roerohan