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_db.py

@@ -2,6 +2,7 @@
 # SPDX-FileCopyrightText: Copyright The LanceDB Authors
 
 
+import contextlib
 import inspect
 import re
 import sys
@@ -405,6 +406,49 @@ async def test_connect(tmp_path):
     assert str(db) == f"ListingDatabase(uri={tmp_path}, read_consistency_interval=5s)"
 
 
+@pytest.fixture(params=["memory", "local", "namespace", "from_inner"])
+def sync_db(request, tmp_path):
+    if request.param == "memory":
+        return lancedb.connect("memory://")
+    if request.param == "namespace":
+        return lancedb.connect_namespace("dir", {"root": str(tmp_path)})
+    db = lancedb.connect(tmp_path)
+    if request.param == "from_inner":
+        return lancedb.db.LanceDBConnection.from_inner(db._inner, None)
+    return db
+
+
+def test_sync_close(sync_db):
+    assert sync_db.is_open()
+    assert sync_db.close() is None
+    assert not sync_db.is_open()
+    assert sync_db.close() is None
+
+    with pytest.warns(DeprecationWarning, match="table_names"):
+        with pytest.raises(RuntimeError, match="Connection is closed"):
+            sync_db.table_names()
+    with pytest.raises(RuntimeError, match="Connection is closed"):
+        sync_db.list_tables()
+    with pytest.raises(RuntimeError, match="Connection is closed"):
+        sync_db.open_table("test")
+
+
+@pytest.mark.parametrize("raise_error", [False, True])
+def test_sync_context_manager(sync_db, raise_error):
+    with contextlib.ExitStack() as stack:
+        if raise_error:
+            stack.enter_context(pytest.raises(ValueError, match="test error"))
+        with sync_db as db:
+            assert db is sync_db
+            assert db.is_open()
+            if raise_error:
+                raise ValueError("test error")
+
+    assert not sync_db.is_open()
+    with pytest.raises(RuntimeError, match="Connection is closed"):
+        sync_db.list_tables()
+
+
 @pytest.mark.asyncio
 async def test_close(mem_db_async: lancedb.AsyncConnection):
     assert mem_db_async.is_open()