gh-116738: Use PyMutex for bz2 module (gh-140555)

The methods are already wrapped with a lock, which makes them thread-safe in
free-threaded build. This replaces `PyThread_acquire_lock` with `PyMutex` and
removes some macros and allocation handling code.

Also add a test for free-threading to ensure we aren't getting data races and
that the locking is working.

Lib/test/test_free_threading/test_bz2.py

@@ -0,0 +1,53 @@
+import unittest
+
+from test.support import import_helper, threading_helper
+from test.support.threading_helper import run_concurrently
+
+bz2 = import_helper.import_module("bz2")
+from bz2 import BZ2Compressor, BZ2Decompressor
+
+from test.test_bz2 import ext_decompress, BaseTest
+
+
+NTHREADS = 10
+TEXT = BaseTest.TEXT
+
+
+@threading_helper.requires_working_threading()
+class TestBZ2(unittest.TestCase):
+    def test_compressor(self):
+        bz2c = BZ2Compressor()
+
+        def worker():
+            # it should return empty bytes as it buffers data internally
+            data = bz2c.compress(TEXT)
+            self.assertEqual(data, b"")
+
+        run_concurrently(worker_func=worker, nthreads=NTHREADS)
+        data = bz2c.flush()
+        # The decompressed data should be TEXT repeated NTHREADS times
+        decompressed = ext_decompress(data)
+        self.assertEqual(decompressed, TEXT * NTHREADS)
+
+    def test_decompressor(self):
+        chunk_size = 128
+        chunks = [bytes([ord("a") + i]) * chunk_size for i in range(NTHREADS)]
+        input_data = b"".join(chunks)
+        compressed = bz2.compress(input_data)
+
+        bz2d = BZ2Decompressor()
+        output = []
+
+        def worker():
+            data = bz2d.decompress(compressed, chunk_size)
+            self.assertEqual(len(data), chunk_size)
+            output.append(data)
+
+        run_concurrently(worker_func=worker, nthreads=NTHREADS)
+        self.assertEqual(len(output), NTHREADS)
+        # Verify the expected chunks (order doesn't matter due to append race)
+        self.assertEqual(set(output), set(chunks))
+
+
+if __name__ == "__main__":
+    unittest.main()