gh-116738: Fix thread-safety issue in re module for free threading (gh-141923)

Added atomic operations to `scanner_begin()` and `scanner_end()` to prevent
race conditions on the `executing` flag in free-threaded builds. Also added
tests for concurrent usage of the `re` module.

Without the atomic operations, `test_scanner_concurrent_access()` triggers
`assert(self->executing)` failures, or a thread sanitizer run emits errors.

Lib/test/test_free_threading/test_re.py

@@ -0,0 +1,62 @@
+import re
+import unittest
+
+from test.support import threading_helper
+from test.support.threading_helper import run_concurrently
+
+
+NTHREADS = 10
+
+
+@threading_helper.requires_working_threading()
+class TestRe(unittest.TestCase):
+    def test_pattern_sub(self):
+        """Pattern substitution should work across threads"""
+        pattern = re.compile(r"\w+@\w+\.\w+")
+        text = "e-mail: test@python.org or user@pycon.org. " * 5
+        results = []
+
+        def worker():
+            substituted = pattern.sub("(redacted)", text)
+            results.append(substituted.count("(redacted)"))
+
+        run_concurrently(worker_func=worker, nthreads=NTHREADS)
+        self.assertEqual(results, [2 * 5] * NTHREADS)
+
+    def test_pattern_search(self):
+        """Pattern search should work across threads."""
+        emails = ["alice@python.org", "bob@pycon.org"] * 10
+        pattern = re.compile(r"\w+@\w+\.\w+")
+        results = []
+
+        def worker():
+            matches = [pattern.search(e).group() for e in emails]
+            results.append(len(matches))
+
+        run_concurrently(worker_func=worker, nthreads=NTHREADS)
+        self.assertEqual(results, [2 * 10] * NTHREADS)
+
+    def test_scanner_concurrent_access(self):
+        """Shared scanner should reject concurrent access."""
+        pattern = re.compile(r"\w+")
+        scanner = pattern.scanner("word " * 10)
+
+        def worker():
+            for _ in range(100):
+                try:
+                    scanner.search()
+                except ValueError as e:
+                    if "already executing" in str(e):
+                        pass
+                    else:
+                        raise
+
+        run_concurrently(worker_func=worker, nthreads=NTHREADS)
+        # This test has no assertions. Its purpose is to catch crashes and
+        # enable thread sanitizer to detect race conditions. While "already
+        # executing" errors are very likely, they're not guaranteed due to
+        # non-deterministic thread scheduling, so we can't assert errors > 0.
+
+
+if __name__ == "__main__":
+    unittest.main()