fix(background-notification): filter unsupported manager events

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/hooks/background-notification/hook.test.ts

@@ -0,0 +1,37 @@
+import { describe, expect, test, mock } from "bun:test"
+
+import { createBackgroundNotificationHook } from "./hook"
+
+describe("createBackgroundNotificationHook", () => {
+  test("#given unsupported event type #when event handler runs #then it does not forward to manager", async () => {
+    //#given
+    const handleEvent = mock(() => {})
+    const hook = createBackgroundNotificationHook({
+      handleEvent,
+      injectPendingNotificationsIntoChatMessage: () => {},
+    } as never)
+
+    //#when
+    await hook.event({ event: { type: "message.removed", properties: { sessionID: "ses-1" } } })
+
+    //#then
+    expect(handleEvent).not.toHaveBeenCalled()
+  })
+
+  test("#given supported event type #when event handler runs #then it forwards to manager", async () => {
+    //#given
+    const handleEvent = mock(() => {})
+    const hook = createBackgroundNotificationHook({
+      handleEvent,
+      injectPendingNotificationsIntoChatMessage: () => {},
+    } as never)
+
+    const event = { type: "message.part.delta", properties: { sessionID: "ses-1", field: "text", delta: "x" } }
+
+    //#when
+    await hook.event({ event })
+
+    //#then
+    expect(handleEvent).toHaveBeenCalledWith(event)
+  })
+})