gh-117440: Make syslog thread-safe in free-threaded builds (#117441)

Use critical sections to protect access to the syslog module.

Modules/syslogmodule.c

@@ -132,6 +132,7 @@ syslog_get_argv(void)
 
 
 /*[clinic input]
+@critical_section
 syslog.openlog
 
     ident: unicode = NULL
@@ -144,7 +145,7 @@ Set logging options of subsequent syslog() calls.
 static PyObject *
 syslog_openlog_impl(PyObject *module, PyObject *ident, long logopt,
                     long facility)
-/*[clinic end generated code: output=5476c12829b6eb75 input=8a987a96a586eee7]*/
+/*[clinic end generated code: output=5476c12829b6eb75 input=ee700b8786f81c23]*/
 {
     // Since the sys.openlog changes the process level state of syslog library,
     // this operation is only allowed for the main interpreter.
@@ -189,6 +190,7 @@ syslog_openlog_impl(PyObject *module, PyObject *ident, long logopt,
 
 
 /*[clinic input]
+@critical_section
 syslog.syslog
 
     [
@@ -205,7 +207,7 @@ Send the string message to the system logger.
 static PyObject *
 syslog_syslog_impl(PyObject *module, int group_left_1, int priority,
                    const char *message)
-/*[clinic end generated code: output=c3dbc73445a0e078 input=ac83d92b12ea3d4e]*/
+/*[clinic end generated code: output=c3dbc73445a0e078 input=6588ddb0b113af8e]*/
 {
     if (PySys_Audit("syslog.syslog", "is", priority, message) < 0) {
         return NULL;
@@ -243,6 +245,7 @@ syslog_syslog_impl(PyObject *module, int group_left_1, int priority,
 
 
 /*[clinic input]
+@critical_section
 syslog.closelog
 
 Reset the syslog module values and call the system library closelog().
@@ -250,7 +253,7 @@ Reset the syslog module values and call the system library closelog().
 
 static PyObject *
 syslog_closelog_impl(PyObject *module)
-/*[clinic end generated code: output=97890a80a24b1b84 input=fb77a54d447acf07]*/
+/*[clinic end generated code: output=97890a80a24b1b84 input=167f489868bd5a72]*/
 {
     // Since the sys.closelog changes the process level state of syslog library,
     // this operation is only allowed for the main interpreter.