Put the cursor in the terminal after sending a note

Sending already switched to the target terminal's tab, which looks like it
should be enough: `TerminalView` focuses xterm whenever a terminal becomes
active. But that effect keys off `active`, so it only fires on a *change* —
and the dock's ordinary case is sending to the terminal already on screen.
`setActiveTabKey` writes the key that is already set, nothing changes, no
effect re-runs, and focus stays on the Send button. The note is sitting in the
prompt and the user still has to click the terminal before pressing Enter.

So the send now asks for focus explicitly, through a one-shot request in the
store that `TerminalView` consumes and clears — the shape `pendingHomeTab`
already uses. Clearing is not tidiness: hold the id and the second send to the
same terminal writes a value that is already there, which is precisely the
no-op this exists to fix.

Focus is requested only on success. A failed send toasts and leaves the user
where they are, because there is nothing in the prompt to press Enter on.

The three `TerminalView` tests give focus away after mounting before making
any assertion, so what they observe is the request landing and never the focus
that `active` already grants on mount — which would pass with the feature
absent.

752 tests pass, 62 files.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011YPqHpjV4EL6RNEwrRKqQm

app/src/components/terminal/TerminalView.test.tsx

@@ -538,3 +538,59 @@ describe("TerminalView — reaching the URL prompt without a mouse", () => {
     expect(document.activeElement).toBe(before);
   });
 });
+
+describe("TerminalView — focus on request", () => {
+  /** Mount, then deliberately give focus away, so what the assertions below
+   *  observe is the *request* taking effect and never the focus `active`
+   *  already grants on mount. That distinction is the whole point: the notes
+   *  dock sends to a terminal whose tab is already active, where nothing
+   *  changes and no `active` effect re-runs. */
+  async function mountAndBlur() {
+    const view = mountSession("claude");
+    await act(async () => {});
+    const elsewhere = document.createElement("button");
+    document.body.appendChild(elsewhere);
+    elsewhere.focus();
+    expect(document.activeElement).toBe(elsewhere);
+    return view;
+  }
+
+  it("focuses the terminal named by the request", async () => {
+    const view = await mountAndBlur();
+
+    await act(async () => {
+      useAppState.getState().requestTerminalFocus("s1");
+    });
+
+    expect(document.activeElement).toBe(helperTextarea(view.container));
+  });
+
+  it("ignores a request meant for another session", async () => {
+    const view = await mountAndBlur();
+    const before = document.activeElement;
+
+    await act(async () => {
+      useAppState.getState().requestTerminalFocus("s2");
+    });
+
+    expect(document.activeElement).toBe(before);
+    expect(document.activeElement).not.toBe(helperTextarea(view.container));
+  });
+
+  it("clears the request, so a second send focuses again", async () => {
+    const view = await mountAndBlur();
+
+    await act(async () => {
+      useAppState.getState().requestTerminalFocus("s1");
+    });
+    expect(useAppState.getState().pendingTerminalFocus).toBeNull();
+
+    const elsewhere = document.querySelector("button");
+    (elsewhere as HTMLButtonElement).focus();
+
+    await act(async () => {
+      useAppState.getState().requestTerminalFocus("s1");
+    });
+    expect(document.activeElement).toBe(helperTextarea(view.container));
+  });
+});