refactor(provider): simplify live_config_managed and deduplicate tolerant live config checks

- Change live_config_managed from Option<bool> to bool with #[serde(default)]
- Extract repeated tolerant live config query into check_live_config_exists helper
- Fix duplicate key generation to also check live-only provider IDs
- Fix updateProvider test to match new { provider, originalId } call signature
- Add streaming_responses test type annotation for compiler inference

tests/hooks/useProviderActions.test.tsx

@@ -169,7 +169,10 @@ describe("useProviderActions", () => {
       await result.current.updateProvider(provider);
     });
 
-    expect(updateProviderMutateAsync).toHaveBeenCalledWith(provider);
+    expect(updateProviderMutateAsync).toHaveBeenCalledWith({
+      provider,
+      originalId: undefined,
+    });
     expect(providersApiUpdateTrayMenuMock).toHaveBeenCalledTimes(1);
   });