(watch) `cdk watch` has no way to write a CloudFormation outputs file (`--outputs-file` and cdk.json `outputsFile` both ignored)

### Summary

There is no supported way to write a CloudFormation outputs file during `cdk watch`. `cdk deploy` writes outputs via either `--outputs-file` or the `cdk.json` `outputsFile` key; `cdk watch` honors **neither**, so a frontend/consumer outputs file can't be kept in sync during a watch session.

**Environment**
- `aws-cdk` (CLI): `2.1128.0` (build 7daa104)
- `aws-cdk-lib`: `2.258.1`
- node: `v24.12.0`
- OS: macOS `26.5.1` (Darwin)

### Reproduction

- `cdk watch --outputs-file out.json` → `Unknown option(s): --outputs-file, --outputsFile. These will be ignored.`
- The `cdk.json` `"outputsFile"` key is **silently ignored** by `cdk watch` (it is honored by `cdk deploy`, verified on `2.1128.0`).

### Expected

`cdk watch` honors `outputsFile` (and/or `--outputs-file`), since it is `cdk deploy --watch` and each watch deployment is a deploy — or the limitation is documented.

### Workaround

Run a `cdk deploy --hotswap --outputs-file ...` once before `cdk watch` to produce the outputs file, then watch for iteration (watch deployments don't change stack outputs).

### Related

- [aws/aws-cdk-cli#1389](https://github.com/aws/aws-cdk-cli/issues/1389) — the separate `cdk deploy --outputs-file` "no file written" regression; appears resolved on 2.1128.0 (the flag does write for `cdk deploy` here), so this issue is specifically about `watch` having no outputs-file mechanism.

Start by tracing the `cdk watch` option parsing and its watch deployment path, then compare how `cdk deploy` handles `--outputs-file` and the `outputsFile` configuration key. Done means watch deployments honor the supported outputs-file configuration or the limitation is documented, with coverage for the reproduced commands.

Written by the indexing model from the issue text.