Updated process starter

[dmytrostruk]

Motivation and Context

Used fully qualified class name in process YAML file.

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows SK Contribution Guidelines (https://github.com/microsoft/semantic-kernel-starters/blob/main/CONTRIBUTING.md)
• The code follows the .NET coding conventions (https://learn.microsoft.com/dotnet/csharp/fundamentals/coding-style/coding-conventions) verified with dotnet format
• All unit tests pass, and I have added new tests where possible
• I didn't break anyone 😄