gh-113964: Don't prevent new threads until all non-daemon threads exit (#116677)

Starting in Python 3.12, we prevented calling fork() and starting new threads
during interpreter finalization (shutdown). This has led to a number of
regressions and flaky tests. We should not prevent starting new threads
(or `fork()`) until all non-daemon threads exit and finalization starts in
earnest.

This changes the checks to use `_PyInterpreterState_GetFinalizing(interp)`,
which is set immediately before terminating non-daemon threads.

Lib/test/test_threading.py

@@ -1154,21 +1154,21 @@ class ThreadTests(BaseTestCase):
         self.assertEqual(out, b'')
         self.assertEqual(err, b'')
 
-    def test_start_new_thread_at_exit(self):
+    def test_start_new_thread_at_finalization(self):
         code = """if 1:
-            import atexit
             import _thread
 
             def f():
                 print("shouldn't be printed")
 
-            def exit_handler():
-                _thread.start_new_thread(f, ())
-
-            atexit.register(exit_handler)
+            class AtFinalization:
+                def __del__(self):
+                    print("OK")
+                    _thread.start_new_thread(f, ())
+            at_finalization = AtFinalization()
         """
         _, out, err = assert_python_ok("-c", code)
-        self.assertEqual(out, b'')
+        self.assertEqual(out.strip(), b"OK")
         self.assertIn(b"can't create new thread at interpreter shutdown", err)
 
 class ThreadJoinOnShutdown(BaseTestCase):
@@ -1297,6 +1297,30 @@ class ThreadJoinOnShutdown(BaseTestCase):
         rc, out, err = assert_python_ok('-c', script)
         self.assertFalse(err)
 
+    def test_thread_from_thread(self):
+        script = """if True:
+            import threading
+            import time
+
+            def thread2():
+                time.sleep(0.05)
+                print("OK")
+
+            def thread1():
+                time.sleep(0.05)
+                t2 = threading.Thread(target=thread2)
+                t2.start()
+
+            t = threading.Thread(target=thread1)
+            t.start()
+            # do not join() -- the interpreter waits for non-daemon threads to
+            # finish.
+            """
+        rc, out, err = assert_python_ok('-c', script)
+        self.assertEqual(err, b"")
+        self.assertEqual(out.strip(), b"OK")
+        self.assertEqual(rc, 0)
+
     @skip_unless_reliable_fork
     def test_reinit_tls_after_fork(self):
         # Issue #13817: fork() would deadlock in a multithreaded program with