[3.11] GH-107518: Remove the Argument Clinic How-To (#109900) (#110761)

(cherry picked from commit d1f7fae424)

* Remove the content of the Argument Clinic HOWTO
* Update cross-references to the Argument Clinic
* Add a note directing readers to the devguide

Co-authored-by: Adam Turner <9087854+AA-Turner@users.noreply.github.com>

Doc/howto/index.rst

@@ -28,7 +28,6 @@ Currently, the HOWTOs are:
    urllib2.rst
    argparse.rst
    ipaddress.rst
-   clinic.rst
    instrumentation.rst
    annotations.rst
    isolating-extensions.rst

Doc/whatsnew/3.8.rst

@@ -123,7 +123,7 @@ There is a new function parameter syntax ``/`` to indicate that some
 function parameters must be specified positionally and cannot be used as
 keyword arguments.  This is the same notation shown by ``help()`` for C
 functions annotated with Larry Hastings'
-:ref:`Argument Clinic <howto-clinic>` tool.
+`Argument Clinic <devguide.python.org/development-tools/clinic/>`__ tool.
 
 In the following example, parameters *a* and *b* are positional-only,
 while *c* or *d* can be positional or keyword, and *e* or *f* are

Misc/NEWS.d/3.11.5.rst

@@ -793,7 +793,7 @@ and 3.1.2.
 
 Argument Clinic now supports overriding automatically generated signature by
 using directive ``@text_signature``. See
-:ref:`clinic-howto-override-signature`.
+`the Argument Clinic docs <devguide.python.org/development-tools/clinic/>`__.
 
 ..