Cut v1.33.13 release

## Scheduled to happen: Thursday, 2026-06-11

## Release Blocking Issues

None

## Release Steps

- [x] Create a thread on #release-management: https://kubernetes.slack.com/archives/CJH2GBF7Y/p1781161590342039
- [x] Screenshot unhealthy release branch testgrid boards
- [x] Check the health of the publishing-bot
- NoMock Run
- [x] Stage
- [x] Image Promotion PR: https://github.com/kubernetes/k8s.io/pull/9592
- [x] Release
- [x] Send email notification: https://groups.google.com/g/kubernetes-announce/c/Y2Rcn2jYa_0/m/sap2P81WAwAJ
- [x] Notify #release-management on Slack: https://kubernetes.slack.com/archives/CJH2GBF7Y/p1781264808916689?thread_ts=1781161590.342039&cid=CJH2GBF7Y
- [x] Update [`schedule.yaml` file](https://github.com/kubernetes/website/blob/main/data/releases/schedule.yaml) with the latest release using [`schedule-builder`](https://github.com/kubernetes/release/tree/master/cmd/schedule-builder) (_patch releases only_)
- [ ] Collect metrics and add them to the `Release steps` table below through `krel history --branch release-1.xx --date-from yyyy-mm-dd` (current date)

## Release Tools Version

```
GitVersion: v0.18.1-0.20260610030544-f8d9e5ca5cc4
GitCommit: f8d9e5ca5cc40956fa2aefa58e4f77e7e132d7c4
GitTreeState: clean
BuildDate: 2026-06-10T03:05:44
GoVersion: go1.26.3
Compiler: gc
Platform: darwin/arm64
```

## Release Jobs History

| Step | Command | Link | Start | Duration | Succeeded? |
| --- | --- | --- | --- | --- | --- |

| Stage | `krel stage [arguments]` | | | | |
| Release | `krel release [arguments]` | | | | |

## Action Items

## Open Questions

/milestone v1.33
/assign
/cc @kubernetes/release-managers
/priority important-soon
/kind documentation