Docs Examples Focus on Outdated Single-Phase Init Modules and Static Types

A variety of pages show examples (or provide explanations) around single-phase init modules and static types, but should focus on the newer, recommended alternatives. For example:

• https://docs.python.org/3/extending/extending.html#intermezzo-errors-and-exceptions
  https://github.com/python/cpython/blob/main/Doc/extending/extending.rst?plain=1#L206-L265
• https://docs.python.org/3/extending/extending.html#the-module-s-method-table-and-initialization-function
  https://github.com/python/cpython/blob/main/Doc/extending/extending.rst?plain=1#L355-L379
• https://docs.python.org/3/extending/newtypes_tutorial.html
  https://github.com/python/cpython/blob/main/Doc/extending/newtypes_tutorial.rst
• https://docs.python.org/3/extending/newtypes.html
  https://github.com/python/cpython/blob/main/Doc/extending/newtypes.rst
• https://docs.python.org/3/extending/embedding.html#extending-embedded-python
  https://github.com/python/cpython/blob/main/Doc/extending/embedding.rst?plain=1#L225

For reference:

• https://docs.python.org/3/howto/isolating-extensions.html#isolating-extensions-howto
• https://docs.python.org/3/c-api/module.html
• https://docs.python.org/3/c-api/type.html#creating-heap-allocated-types

Linked PRs

• gh-134296
• gh-134753
• gh-134754
• gh-134764
• gh-134773
• gh-134775
• gh-134827
• gh-134828
• gh-134932
• gh-134983
• gh-135126
• gh-135174
• gh-135213
• gh-135214
• gh-135470
• gh-140214
• gh-140664
• gh-142314
• gh-144183

Start by comparing the cited sections in Doc/extending/extending.rst, newtypes_tutorial.rst, newtypes.rst, and embedding.rst with the isolating extensions, module, and type references. Identify which examples and explanations still use single-phase initialization or static types, then update them to the recommended alternatives and verify all listed documentation pages are consistent.