[Function Request] NOTTE__RUN_FUNCTION (extends existing Notte app)

### Required Pre-requisites

- [x] I have read the [Documentation](https://www.aci.dev/docs)
- [x] I have searched the [Issue Tracker](https://github.com/aipotheosis-labs/aci/issues)
- [x] I have searched the [apps directory](https://github.com/aipotheosis-labs/aci/tree/main/backend/apps) to see if this integration already exists

### App Name

Notte (existing app at `backend/apps/notte/`)

### Function Name

NOTTE__RUN_FUNCTION

### API Docs Link

https://docs.notte.cc/api-reference/functions/function-run-start

### Additional Context

The existing Notte integration in ACI (`backend/apps/notte/`) wraps 3 page-scraping primitives: `NOTTE__START_SESSION`, `NOTTE__OBSERVE_PAGE`, `NOTTE__SCRAPE_DATA`. It does not expose **Notte Functions**, the deploy-a-browser-script-as-an-API capability that shipped after the v1.0.0 wrapper.

A Notte Function is a serverless deployment of a browser automation script. Once deployed (one-time, via Notte SDK), it has a stable `function_id` and accepts arbitrary parameters as JSON. With this wrapper, an ACI user can:

1. Author a custom browser flow (book a flight, monitor stock, fill a form, scrape a paywalled feed) as a Notte Function once.
2. Register the resulting `function_id` as an ACI tool (via this new wrapper).
3. Have any ACI agent invoke it like any other tool, with deterministic execution and lower per-call cost than re-running an exploratory browser-use agent.

The wrapper is a single REST call:

```
POST https://api.notte.cc/functions/{function_id}/runs/start
Authorization: Bearer NOTTE_API_KEY
Body: { "": ... }
```

**Use case:** ACI users with recurring browser tasks (vendor-specific dashboards, supplier portals, paywalled data feeds) can deploy each flow once on Notte, then call them through ACI as named tools. Reduces token cost and latency vs. agent-per-call.

**Reference:** this is the same value prop we're staging for NousResearch/hermes-agent ([nottelabs/notte#758](https://github.com/nottelabs/notte/pull/758), open PR with the provider class, unit tests, and the upstream integration guide — Mendral-approved, currently finishing CI before merge into our staging repo) — Notte as the deployment surface for browser flows that outlive a single agent run.

Happy to PR the wrapper ourselves following ACI's existing patterns in `backend/apps/notte/functions.json` if that is preferred over having your team write it.