Introduce a new game type named Game5x3 that supports 5 colors and 3 fields.

Tasks

• Implement the new game configuration (5 colors, 3 fields).
• Update the analyzer to support this game logic, including validation and scoring.
• Adjust API endpoints to allow creating and interacting with Game5x3.
• Update bot logic and game flow for the new type.
• Add or update tests to ensure coverage for Game5x3.

Additional notes

• Use C# modern features (collection expressions, pattern matching, primary constructors where possible).
• Ensure all relevant game logic and components are updated.
• Update documentation if needed.