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/c-api/exceptions.rst

@@ -602,7 +602,7 @@ Signal Handling
 .. c:function:: int PyErr_CheckSignals()
 
    .. index::
-      module: signal
+      pair: module; signal
       single: SIGINT
       single: KeyboardInterrupt (built-in exception)
 
@@ -633,7 +633,7 @@ Signal Handling
 .. c:function:: void PyErr_SetInterrupt()
 
    .. index::
-      module: signal
+      pair: module; signal
       single: SIGINT
       single: KeyboardInterrupt (built-in exception)
 
@@ -648,7 +648,7 @@ Signal Handling
 .. c:function:: int PyErr_SetInterruptEx(int signum)
 
    .. index::
-      module: signal
+      pair: module; signal
       single: KeyboardInterrupt (built-in exception)
 
    Simulate the effect of a signal arriving. The next time

Doc/c-api/init.rst

@@ -336,9 +336,9 @@ Initializing and finalizing the interpreter
       single: PyEval_InitThreads()
       single: modules (in module sys)
       single: path (in module sys)
-      module: builtins
-      module: __main__
-      module: sys
+      pair: module; builtins
+      pair: module; __main__
+      pair: module; sys
       triple: module; search; path
       single: PySys_SetArgv()
       single: PySys_SetArgvEx()
@@ -1051,7 +1051,7 @@ code, or when embedding the Python interpreter:
 
    .. deprecated:: 3.9
 
-   .. index:: module: _thread
+   .. index:: pair: module; _thread
 
 
 .. c:function:: int PyEval_ThreadsInitialized()
@@ -1494,9 +1494,9 @@ function. You can create and destroy them using the following functions:
 .. c:function:: PyThreadState* Py_NewInterpreter()
 
    .. index::
-      module: builtins
-      module: __main__
-      module: sys
+      pair: module; builtins
+      pair: module; __main__
+      pair: module; sys
       single: stdout (in module sys)
       single: stderr (in module sys)
       single: stdin (in module sys)

Doc/c-api/intro.rst

@@ -705,9 +705,9 @@ interpreter can only be used after the interpreter has been initialized.
 
 .. index::
    single: Py_Initialize()
-   module: builtins
-   module: __main__
-   module: sys
+   pair: module; builtins
+   pair: module; __main__
+   pair: module; sys
    triple: module; search; path
    single: path (in module sys)