Feature/sam 260011:[WIP]Move all folders to sample

[Heisenberg208]

Description

Refactored API routing to separate greet into its own router for selective inclusion while keeping existing API endpoints under the versioned prefix.

Added proper router mounting and clarified root behavior to avoid path conflicts and unintended 404s.

Improved route organization for cleaner namespace management and better extensibility moving forward.
Fixes #12 (issue)

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

Checklist

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules
• I have checked my code and corrected any misspellings