fix(provider): distinguish legacy providers from db-only when tolerating live config errors

Change `ProviderMeta.live_config_managed` from `bool` to `Option<bool>`
to introduce a three-state semantic:
- `Some(true)`: provider has been written to live config
- `Some(false)`: explicitly db-only, never written to live config
- `None`: legacy data or unknown state (pre-existing providers)

Previously, legacy providers defaulted to `live_config_managed = false`
via `#[serde(default)]`, which silently swallowed live config parse
errors. This could mask genuine configuration issues for providers that
had actually been synced to live config before the field was introduced.

Now, only providers with an explicit `Some(false)` marker tolerate parse
errors; legacy `None` providers surface errors as before, preserving
safety for already-managed configurations.

Also wrap the `ensureQueryData` call for live provider IDs during
duplication in a try/catch so that a malformed config file shows a
user-facing toast instead of silently failing.

Add tests for both the legacy error propagation path and the frontend
duplication failure scenario.

tests/integration/App.test.tsx

@@ -2,6 +2,7 @@ import { Suspense, type ComponentType } from "react";
 import { QueryClient, QueryClientProvider } from "@tanstack/react-query";
 import { render, screen, waitFor, fireEvent } from "@testing-library/react";
 import { describe, it, expect, beforeEach, vi } from "vitest";
+import { providersApi } from "@/lib/api/providers";
 import {
   resetProviderState,
   setCurrentProviderId,
@@ -282,4 +283,52 @@ describe("App integration with MSW", () => {
       expect.stringContaining("Provider key is required for openclaw"),
     );
   });
+
+  it("shows toast when duplicate cannot load live provider ids", async () => {
+    setProviders("openclaw", {
+      deepseek: {
+        id: "deepseek",
+        name: "DeepSeek",
+        settingsConfig: {
+          baseUrl: "https://api.deepseek.com",
+          apiKey: "test-key",
+          api: "openai-completions",
+          models: [],
+        },
+        category: "custom",
+        sortIndex: 0,
+        createdAt: Date.now(),
+      },
+    });
+    setCurrentProviderId("openclaw", "deepseek");
+
+    const liveIdsSpy = vi
+      .spyOn(providersApi, "getOpenClawLiveProviderIds")
+      .mockRejectedValueOnce(new Error("broken config"));
+
+    const { default: App } = await import("@/App");
+    renderApp(App);
+
+    fireEvent.click(screen.getByText("switch-openclaw"));
+
+    await waitFor(() =>
+      expect(screen.getByTestId("provider-list").textContent).toContain(
+        "deepseek",
+      ),
+    );
+
+    fireEvent.click(screen.getByText("duplicate"));
+
+    await waitFor(() => {
+      expect(toastErrorMock).toHaveBeenCalledWith(
+        expect.stringContaining("读取配置中的供应商标识失败"),
+      );
+    });
+
+    expect(screen.getByTestId("provider-list").textContent).not.toContain(
+      "deepseek-copy",
+    );
+
+    liveIdsSpy.mockRestore();
+  });
 });