[Bug]: Issue with pkgdown workflow

### What happened?

Heya, We are currently using the `pkgdown.yaml` but it appears to be broken for us.

Our setup is just the stock
```
docs:
name: Pkgdown Docs 📚
needs: release
uses: insightsengineering/r.pkg.template/.github/workflows/pkgdown.yaml@main
secrets:
REPO_GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
with:
default-landing-page: "latest-tag"
```
https://github.com/gowerc/diffdf/blob/master/.github/workflows/release.yaml

However we are now getting the following errors after pushing to master

```
[gh-pages 3d7894f] [actions skip] Built site for diffdf@ca1b5331ec567d3450660251f21853937b2436dc
Author: gowerc <8447209+gowerc@users.noreply.github.com>
54 files changed, 3230 insertions(+), 1012 deletions(-)
INPUT_TAGGING_MESSAGE:
No tagging message supplied. No tag will be added.
INPUT_PUSH_OPTIONS:
error: atomic push failed for ref refs/heads/gh-pages. status: 5
To https://github.com/gowerc/diffdf
! [rejected] HEAD -> gh-pages (fetch first)
error: failed to push some refs to 'https://github.com/gowerc/diffdf'
hint: Updates were rejected because the remote contains work that you do not
hint: have locally. This is usually caused by another repository pushing to
hint: the same ref. If you want to integrate the remote changes, use
hint: 'git pull' before pushing again.
hint: See the 'Note about fast-forwards' in 'git push --help' for details.
Error: Invalid status code: 1
at ChildProcess. (/home/runner/work/_actions/stefanzweifel/git-auto-commit-action/v5/index.js:17:19)
at ChildProcess.emit (node:events:524:28)
at maybeClose (node:internal/child_process:1104:16)
at ChildProcess._handle.onexit (node:internal/child_process:304:5) {
code: 1
}
Error: Invalid status code: 1
at ChildProcess. (/home/runner/work/_actions/stefanzweifel/git-auto-commit-action/v5/index.js:17:19)
at ChildProcess.emit (node:events:524:28)
at maybeClose (node:internal/child_process:1104:16)
at ChildProcess._handle.onexit (node:internal/child_process:304:5)
```
https://github.com/gowerc/diffdf/actions/runs/18620379110/job/53090832071

Any ideas ?

### Which version(s) of R were you using?

Other

### Relevant log output

```R

```

### Code of Conduct

- [x] I agree to follow this project's Code of Conduct.

### Contribution Guidelines

- [x] I agree to follow this project's Contribution Guidelines.