code-style has different behavior between uv and poetry backends

### 🔍 Before submitting the issue

- [x] I have searched among the existing issues
- [x] I am using a Python virtual environment

### 🐞 Description of the bug

If code-style is run on a project using poetry, and `skip-install` is set to False, then the entire project is installed with all dependencies:

https://github.com/ansys/actions/blob/1240aef678c0335bbc502c6f8097e17d1e514246/code-style/action.yml#L239

If however, code-style is run on a project using uv with the same configuration, then only the dependencies in the wheel are installed:

https://github.com/ansys/actions/blob/1240aef678c0335bbc502c6f8097e17d1e514246/code-style/action.yml#L241

We were previously depending on the poetry behavior, because as part of the project installation we install mypy as a dev dependency. mypy needs to be installed in the environment itself to work. Since mypy is a dev dependency, it's installed with a poetry project, but not installed with a uv project.

uv should probably just do a `uv sync`, such that the behavior is more similar to the poetry case.

### 📝 Steps to reproduce

See an example here https://github.com/ansys-internal/grantami-system/actions/runs/16201141925/job/45740217086 of CI running, where mypy is not available after project install

### 💻 Which operating system are you using?

Windows

### 📀 Which ANSYS version are you using?

N/A

### 🐍 Which Python version are you using?

3.12

### 📦 Installed packages

```shell
Actions v10.0.12
```

Start in code-style/action.yml at the installation commands around lines 239 and 241, comparing the Poetry and uv backend paths when skip-install is false. Reproduce the Windows/Python 3.12 case from the linked grantami-system CI run and verify that the uv path makes mypy available after project installation, matching the Poetry behavior.

Written by the indexing model from the issue text.