Part of #40269
cc: @tscrim

This PR introduces a new base class, FanoToricVariety_field, which represents Gorenstein Fano toric varieties—toric varieties with ample Cartier anticanonical divisors. It serves as a superclass for the existing CPRFanoToricVariety_field and a forthcoming SmoothFanoToricVariety_field.

Mathematically, this reflects the natural inclusion hierarchy:
$$\text{smooth Fano} \subset \text{Gorenstein (reflexive) Fano} \subset \text{ℚ‑Fano}$$

• The FanoToricVariety_field class abstracts the common functionality of Gorenstein Fano varieties constructed from reflexive polytopes.
• The existing CPRFanoToricVariety_field (based on crepant partial resolutions) is refactored to inherit from this new base class.
• Future smooth Fano varieties (from smooth reflexive polytopes) will also extend from this class.
• Existing methods such as cartesian_product, anticanonical_hypersurface, and nef_complete_intersection, previously defined only for CPR-Fano varieties, are now lifted to the new base class, as they are valid and important in the broader Gorenstein Fano context.

The core distinction between the classes lies in the fan construction:

• CPR-Fano varieties use crepant subdivisions of the normal fan by adding interior lattice points.
• Fano varieties use the normal fan of polar of reflexive polytopes, no refinement
• Smooth Fano varieties use fans from smooth reflexive polytopes, hence no resolution is required.

ToricVariety_field
├── FanoToricVariety_field        # New base class: assumes ample Cartier -K_X
│   ├── CPRFanoToricVariety_field           # Subclass: uses crepant partial resolution via coordinate_points
│   └── SmoothFanoToricVariety_field        # Subclass: assumes smooth fan directly

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies