DOC: Add direct C-extension testing guide - #20239

Description

Hi everyone!!

This PR adds TESTING_EXTENSIONS.rst to the developer docs and wires it up in index_dev.rst.

Over the course of my GSoC project, I've been writing a lot of tests for our C and Cython extensions. Since establishing this direct test layer is a big prerequisite for safely splitting the low-level layer into a separate package (the APE split), I wanted to put together a proper guide on how to test these compiled modules directly and in pure isolation.

Here is a quick rundown of what the guide covers:

• How to bypass high-level Python wrappers and hit the C-slots directly using minimal shims and .view() casting.
• Why we need to use strict type() checks instead of isinstance() at the C-boundary, and guidelines for using numpy.typing.NDArray.
• Tips for exhaustive structural validation, using zip(..., strict=True), and handling tricky edge cases like explosive memory allocations and np.nan.
• Best practices for catching and safely validating C-level crashes across the Python boundary using substring matching.
• Architectural rules for static analysis, like locking dimensions with TypeVar and enforcing positional-only arguments.

I'd really love to get your thoughts on this! Please let me know if anything feels off, if the tone works, or if there are any sections that need more clarity. Looking forward to any suggested changes or improvements, I'm more than happy to iterate on this to make sure it's as helpful as possible for future contributors.

Related Issues

• Relates to GSoC 2026 Proposal: Hardening Astropy's Core Stability

cc: @neutrinoceros