Hugo v0.134.3 - GitHub action fails to build

**Describe the bug**

While testing a hugo + static web app deployment yesterday, I ran into an issue where the github action fails to build.
I've re-created the repo twice, and got the same issue. There is a public version here: https://github.com/builtwithcaffeine/static-web-app-demo-two

A clear and concise description of what the bug is.

**To Reproduce**
Steps to reproduce the behavior:
1. Create Azure Static Web App + GitHub Repository
2. Clone and create new site: `hugo new site static-web-app-demo-two --force`
3. Push content to GitHub
4. Configure Static Web App
5. Watch Build and see error - see error


https://github.com/builtwithcaffeine/static-web-app-demo-two/actions/runs/10955654558/job/30420004780

**Expected behavior**
During the github action build process the contents of the hugo static web app should be uploaded into the Azure Static Web App.
Build time should take around 2 minutes for a basic site and then the app should be visible online.

**Additional context**
Add any other context about the problem here.

Looking at the Bilberry theme - https://github.com/Lednerb/bilberry-hugo-theme, there was a recent patch for .Site.IsServer compatibility - https://github.com/Lednerb/bilberry-hugo-theme/issues/655
```
ERROR deprecated: .Site.IsServer was deprecated in Hugo v0.120.0 and will be removed in Hugo 0.135.0. Use hugo.IsServer instead.
Built in 168 ms
Error: error building site: logged 1 error(s)
```
I notice that when the github action builds, it still using hugo 1.12. But I'm not sure if this is the cause of the issue.
I've also tried with the same latest theme using submodule and downloaded the zip and uploaded all files