fix(python): close synchronous database connections (#4424)

Calling `close()` on a synchronous remote connection returned an
unawaited coroutine and left the connection usable. Local synchronous
connections had no close or context-manager API.

Add synchronous `close()` and `is_open()` to the connection interface,
delegate them to the existing connection handle for local, remote, and
namespace connections, and provide shared context-manager cleanup.
Closing is idempotent, and subsequent database operations use the
existing `Connection is closed` error. Document the lifecycle with
examples.

Validation:

- Reproduced the reported coroutine warning and missing local lifecycle
API on the original code; all 15 new regression cases failed before the
fix.
- All 168 tests in `test_db.py`, `test_remote_db.py`, and
`test_namespace.py` passed through the uv-managed environment, including
local, in-memory, namespace, native-derived, and mocked remote lifecycle
coverage.
- All 6 synchronous connection doctests passed.
- Repository-wide Ruff 0.9.9 lint and formatting passed; `git diff
--check` passed.

Fixes #4382

<!-- lance-gatekeeper-fix:v1 agent=a743139af98198f1d4c8934c9cc1d0c9
generation=1 -->

Co-authored-by: Gatefixer <313497061+lancedb-gatefixer[bot]@users.noreply.github.com>

python/python/tests/test_remote_db.py

@@ -2145,15 +2145,46 @@ async def test_header_provider_overrides_static_headers():
 
 
 def test_close():
-    """Test that close() works without AttributeError."""
-    import asyncio
-
     def handler(req):
         req.send_response(200)
         req.end_headers()
 
     with mock_lancedb_connection(handler) as db:
-        asyncio.run(db.close())
+        assert db.close() is None
+        assert not db.is_open()
+        assert db.close() is None
+
+        with pytest.warns(DeprecationWarning, match="table_names"):
+            with pytest.raises(RuntimeError, match="Connection is closed"):
+                db.table_names()
+        with pytest.raises(RuntimeError, match="Connection is closed"):
+            db.list_tables()
+        with pytest.raises(RuntimeError, match="Connection is closed"):
+            db.open_table("test")
+
+
+@pytest.mark.parametrize("raise_error", [False, True])
+def test_sync_context_manager(raise_error):
+    def handler(req):
+        req.send_response(200)
+        req.send_header("Content-Type", "application/json")
+        req.end_headers()
+        req.wfile.write(b'{"tables": []}')
+
+    with mock_lancedb_connection(handler) as db:
+        with contextlib.ExitStack() as stack:
+            if raise_error:
+                stack.enter_context(pytest.raises(ValueError, match="test error"))
+            with db as conn:
+                assert conn is db
+                assert conn.is_open()
+                assert conn.list_tables().tables == []
+                if raise_error:
+                    raise ValueError("test error")
+
+        assert not db.is_open()
+        with pytest.raises(RuntimeError, match="Connection is closed"):
+            db.list_tables()
 
 
 @pytest.mark.parametrize("exception", [KeyboardInterrupt, SystemExit, GeneratorExit])