Show task notifications as synthetic tool calls in chat (#79)

* fix(server): render claude task notifications as synthetic tool calls

* refactor(claude): extract task-notification tool-call mapper

* refactor: drive tool icons from plain_text detail metadata

* refactor(claude): make task-notification parsing schema-first

packages/app/src/utils/tool-call-icon.test.ts

@@ -7,6 +7,7 @@ const iconMocks = vi.hoisted(() => ({
   MicVocal: () => null,
   Pencil: () => null,
   Search: () => null,
+  Sparkles: () => null,
   SquareTerminal: () => null,
   Wrench: () => null,
 }));
@@ -48,4 +49,24 @@ describe("tool-call-icon", () => {
 
     expect(icon).toBe(iconMocks.Brain);
   });
+
+  it("uses custom icon from plain_text detail", () => {
+    const icon = resolveToolCallIcon("custom_tool", {
+      type: "plain_text",
+      label: "Background task completed",
+      icon: "sparkles",
+      text: "notification payload",
+    });
+
+    expect(icon).toBe(iconMocks.Sparkles);
+  });
+
+  it("does not special-case skill tool names", () => {
+    const icon = resolveToolCallIcon("skill", {
+      type: "plain_text",
+      label: "Skill output",
+    });
+
+    expect(icon).toBe(iconMocks.Wrench);
+  });
 });