GH-97950: Use new-style index directive ('module') (#103996)

* Use new-style index directive ('module') - C API

* Use new-style index directive ('module') - Library

* Use new-style index directive ('module') - Reference

* Use new-style index directive ('module') - Tutorial

* Uncomment module removal in pairindextypes

* Use new-style index directive ('module') - C API

* Use new-style index directive ('module') - Library

* Use new-style index directive ('module') - Reference

Doc/reference/compound_stmts.rst

@@ -297,7 +297,7 @@ traceback attached to them, they form a reference cycle with the stack frame,
 keeping all locals in that frame alive until the next garbage collection occurs.
 
 .. index::
-   module: sys
+   pair: module; sys
    object: traceback
 
 Before an :keyword:`!except` clause's suite is executed,

Doc/reference/datamodel.rst

@@ -377,7 +377,7 @@ Sequences
          (and hence unhashable), byte arrays otherwise provide the same interface
          and functionality as immutable :class:`bytes` objects.
 
-      .. index:: module: array
+      .. index:: pair: module; array
 
       The extension module :mod:`array` provides an additional example of a
       mutable sequence type, as does the :mod:`collections` module.
@@ -451,8 +451,8 @@ Mappings
       section :ref:`dict`).
 
       .. index::
-         module: dbm.ndbm
-         module: dbm.gnu
+         pair: module; dbm.ndbm
+         pair: module; dbm.gnu
 
       The extension modules :mod:`dbm.ndbm` and :mod:`dbm.gnu` provide
       additional examples of mapping types, as does the :mod:`collections`
@@ -909,7 +909,7 @@ Class instances
 I/O objects (also known as file objects)
    .. index::
       builtin: open
-      module: io
+      pair: module; io
       single: popen() (in module os)
       single: makefile() (socket method)
       single: sys.stdin

Doc/reference/executionmodel.rst

@@ -151,7 +151,7 @@ to previously bound variables in the nearest enclosing function scope.
 :exc:`SyntaxError` is raised at compile time if the given name does not
 exist in any enclosing function scope.
 
-.. index:: module: __main__
+.. index:: pair: module; __main__
 
 The namespace for a module is automatically created the first time a module is
 imported.  The main module for a script is always called :mod:`__main__`.

Doc/reference/toplevel_components.rst

@@ -21,9 +21,9 @@ Complete Python programs
 .. index:: single: program
 
 .. index::
-   module: sys
-   module: __main__
-   module: builtins
+   pair: module; sys
+   pair: module; __main__
+   pair: module; builtins
 
 While a language specification need not prescribe how the language interpreter
 is invoked, it is useful to have a notion of a complete Python program.  A
@@ -38,7 +38,7 @@ the next section.
 
 .. index::
    single: interactive mode
-   module: __main__
+   pair: module; __main__
 
 The interpreter may also be invoked in interactive mode; in this case, it does
 not read and execute a complete program but reads and executes one statement