fix(webui): keep composer model badge in sync

webui/src/components/thread/ThreadShell.tsx

@@ -195,7 +195,7 @@ function toModelBadgeInfo(
   const preset = modelPresetForBadge(settings, scopedPreset);
   const model = scopedPreset
     ? preset?.model || null
-    : modelName || settings?.agent.model || null;
+    : settings?.agent.model || modelName || null;
   const label = toModelBadgeLabel(model);
   const rawProvider = preset?.provider
     || (!scopedPreset ? settings?.agent.provider : null)

webui/src/tests/thread-shell.test.tsx

@@ -369,6 +369,26 @@ describe("ThreadShell", () => {
     expect(await screen.findByTestId("composer-model-logo-openai_codex")).toBeInTheDocument();
   });
 
+  it("keeps the composer model name and provider on the same settings snapshot", async () => {
+    const client = makeClient();
+    render(
+      wrap(
+        client,
+        <ThreadShell
+          session={session("model-settings-sync")}
+          title="Model settings sync"
+          onToggleSidebar={() => {}}
+          settingsSnapshot={modelSettings("openai-codex/gpt-5.5", "openai_codex")}
+        />,
+        "ling/ling-3.0-flash",
+      ),
+    );
+
+    expect(await screen.findByTestId("composer-model-logo-openai_codex")).toBeInTheDocument();
+    expect(screen.getByText("gpt-5.5")).toBeInTheDocument();
+    expect(screen.queryByText("ling-3.0-flash")).not.toBeInTheDocument();
+  });
+
   it("resolves the composer model from the active session preset", async () => {
     const client = makeClient();
     render(