feat: add check_exist tool

SYNO.FileStation.CheckExist returns error 400 for every parameter format on
this DSM firmware, so the tool falls back to SYNO.FileStation.List::getinfo.
DSM returns an entry per requested path with name=None for non-existent paths,
which provides a reliable exists/not-exists signal.

Accepts a single path or a comma-separated list; returns a table of
Path | Exists (Yes/No) with a count footer.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

tests/test_tools_filestation.py

@@ -1075,3 +1075,125 @@ async def test_upload_dsm_error(config: AppConfig) -> None:
 
     assert result.startswith("Error:")
     assert "permission" in result.lower()
+
+
+# ──────────────────────────────────────────────────────────────────────────
+# check_exist
+# ──────────────────────────────────────────────────────────────────────────
+
+
+@pytest.mark.asyncio
+async def test_check_exist_single_existing(config: AppConfig) -> None:
+    """check_exist returns Yes for a path that exists."""
+    client = MagicMock()
+    client.request = AsyncMock(
+        return_value={
+            "files": [
+                {"path": "/docker", "name": "docker", "isdir": True, "additional": {}},
+            ]
+        }
+    )
+
+    tools = _make_mcp_and_tools(config, client)
+    result = await tools["check_exist"](path="/docker")
+
+    assert "/docker" in result
+    assert "Yes" in result
+    assert "No" not in result
+    assert "1 path(s) checked" in result
+
+
+@pytest.mark.asyncio
+async def test_check_exist_single_missing(config: AppConfig) -> None:
+    """check_exist returns No for a path that does not exist (name=None from DSM)."""
+    client = MagicMock()
+    client.request = AsyncMock(
+        return_value={
+            "files": [
+                {"path": "/no-such-path", "name": None, "isdir": None, "additional": None},
+            ]
+        }
+    )
+
+    tools = _make_mcp_and_tools(config, client)
+    result = await tools["check_exist"](path="/no-such-path")
+
+    assert "/no-such-path" in result
+    assert "No" in result
+    assert "1 path(s) checked" in result
+
+
+@pytest.mark.asyncio
+async def test_check_exist_multi_path(config: AppConfig) -> None:
+    """check_exist handles comma-separated paths and reports each correctly."""
+    client = MagicMock()
+    client.request = AsyncMock(
+        return_value={
+            "files": [
+                {"path": "/docker", "name": "docker", "isdir": True, "additional": {}},
+                {"path": "/ghost", "name": None, "isdir": None, "additional": None},
+            ]
+        }
+    )
+
+    tools = _make_mcp_and_tools(config, client)
+    result = await tools["check_exist"](path="/docker,/ghost")
+
+    assert "/docker" in result
+    assert "/ghost" in result
+    assert "Yes" in result
+    assert "No" in result
+    assert "2 path(s) checked" in result
+
+    # Verify DSM was called with both paths as a JSON array
+    call_params = client.request.call_args[1]["params"]
+    requested_paths = json.loads(call_params["path"])
+    assert "/docker" in requested_paths
+    assert "/ghost" in requested_paths
+
+
+@pytest.mark.asyncio
+async def test_check_exist_empty_path(config: AppConfig) -> None:
+    """check_exist returns Error: when no path is given."""
+    client = MagicMock()
+    client.request = AsyncMock()
+
+    tools = _make_mcp_and_tools(config, client)
+    result = await tools["check_exist"](path="   ")
+
+    assert result.startswith("Error:")
+    client.request.assert_not_called()
+
+
+@pytest.mark.asyncio
+async def test_check_exist_dsm_error(config: AppConfig) -> None:
+    """check_exist propagates DSM errors as Error: messages."""
+    client = MagicMock()
+    client.request = AsyncMock(side_effect=SynologyError("Permission denied", code=105))
+
+    tools = _make_mcp_and_tools(config, client)
+    result = await tools["check_exist"](path="/docker")
+
+    assert result.startswith("Error:")
+    assert "Permission denied" in result
+
+
+@pytest.mark.asyncio
+async def test_check_exist_uses_getinfo(config: AppConfig) -> None:
+    """check_exist uses SYNO.FileStation.List::getinfo as its DSM backend."""
+    client = MagicMock()
+    client.request = AsyncMock(
+        return_value={
+            "files": [
+                {"path": "/docker", "name": "docker", "isdir": True, "additional": {}},
+            ]
+        }
+    )
+
+    tools = _make_mcp_and_tools(config, client)
+    await tools["check_exist"](path="/docker")
+
+    client.request.assert_called_once()
+    call_args = client.request.call_args
+    assert call_args[0][0] == "SYNO.FileStation.List"
+    assert call_args[0][1] == "getinfo"