docs: show nogil in most examples

[henryiii]

Now that free-threading is no longer experimental, I think we should either always show it, or switch the default to on with a way to opt-out instead. Always showing it doesn't require a bump, so maybe we do that for now?

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Created using mini-swe-agent and the propmt:

I'd like to find usages of PYBIND11_MODULE in the docs folder and add py::mod_gil_not_used() as a third argument if there ar
e only two arguments. These are examples, and it's really a good idea to always include that now.

I removed a few of the changes.

Signed-off-by: Henry Schreiner [email protected]

Description

Suggested changelog entry:

• Show nogil in most examples.

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📚 Documentation preview 📚: https://pybind11--5770.org.readthedocs.build/

[rwgk]

@b-pass Here is another Python 3.12 tlock.locked() flake:

https://github.com/pybind/pybind11/actions/runs/16547614513/job/46797808085?pr=5770

cd /home/runner/work/pybind11/pybind11/build/tests/test_embed && /home/runner/work/pybind11/pybind11/build/tests/test_embed/test_embed
Exception ignored in: <module 'threading' from '/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/threading.py'>
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/threading.py", line 1602, in _shutdown
    assert tlock.locked()
           ^^^^^^^^^^^^^^
AssertionError: 
munmap_chunk(): invalid pointer