gh-140727: Restructure profiling documentation for PEP 799 (#142373)

* Add profiling module documentation structure

PEP 799 introduces a new `profiling` package that reorganizes Python's
profiling tools under a unified namespace. This commit adds the documentation
structure to match: a main entry point (profiling.rst) that helps users choose
between profilers, detailed docs for the tracing profiler (profiling-tracing.rst),
and separated pstats documentation.

The tracing profiler docs note that cProfile remains as a backward-compatible
alias, so existing code continues to work. The pstats module gets its own page
since it's used by both profiler types and deserves focused documentation.

* Add profiling.sampling documentation

The sampling profiler is new in Python 3.15 and works fundamentally differently
from the tracing profiler. It observes programs from outside by periodically
capturing stack snapshots, which means zero overhead on the profiled code. This
makes it practical for production use where you can attach to live servers.

The docs explain the key concepts (statistical vs deterministic profiling),
provide quick examples upfront, document all output formats (pstats, flamegraph,
gecko, heatmap), and cover the live TUI mode. The defaults table helps users
understand what happens without any flags.

* Wire profiling docs into the documentation tree

Add the new profiling module pages to the Debugging and Profiling toctree.
The order places the main profiling.rst entry point first, followed by the
two profiler implementations, then pstats, and finally the deprecated profile
module last.

* Convert profile.rst to deprecation stub

The pure Python profile module is deprecated in 3.15 and scheduled for removal
in 3.17. Users should migrate to profiling.tracing (or use the cProfile alias
which continues to work).

The page now focuses on helping existing users migrate: it shows the old vs new
import style, keeps the shared API reference since both modules have the same
interface, and preserves the calibration docs for anyone still using the pure
Python implementation during the transition period.

* Update CLI module references for profiling restructure

Point cProfile to profiling.tracing docs and add profiling.sampling to the
list of modules with CLI interfaces. The old profile-cli label no longer
exists after the documentation restructure.

* Update whatsnew to link to profiling module docs

Enable cross-references to the new profiling module documentation and update
the CLI examples to use the current syntax with the attach subcommand. Also
reference profiling.tracing instead of cProfile since that's the new canonical
name.

Author: pablogsal

Doc/library/cmdline.rst

@@ -12,7 +12,7 @@ The following modules have a command-line interface.
 * :ref:`calendar <calendar-cli>`
 * :mod:`code`
 * :ref:`compileall <compileall-cli>`
-* :mod:`cProfile`: see :ref:`profile <profile-cli>`
+* ``cProfile``: see :ref:`profiling.tracing <profiling-tracing-cli>`
 * :ref:`dis <dis-cli>`
 * :ref:`doctest <doctest-cli>`
 * :mod:`!encodings.rot_13`
@@ -31,8 +31,9 @@ The following modules have a command-line interface.
 * :ref:`pickletools <pickletools-cli>`
 * :ref:`platform <platform-cli>`
 * :mod:`poplib`
-* :ref:`profile <profile-cli>`
-* :mod:`pstats`
+* :ref:`profiling.sampling <profiling-sampling>`
+* :ref:`profiling.tracing <profiling-tracing-cli>`
+* :ref:`pstats <pstats-cli>`
 * :ref:`py_compile <py_compile-cli>`
 * :mod:`pyclbr`
 * :mod:`pydoc`

Doc/library/debug.rst

@@ -1,5 +1,5 @@
 ***********************
-Debugging and Profiling
+Debugging and profiling
 ***********************
 
 These libraries help you with Python development: the debugger enables you to
@@ -15,7 +15,8 @@ intrusive debugging or patching.
    bdb.rst
    faulthandler.rst
    pdb.rst
-   profile.rst
+   profiling.rst
+   pstats.rst
    timeit.rst
    trace.rst
    tracemalloc.rst