fix(sidebar): cancel pending debounce emit on external value reset (#1244)

SidebarSearch's value-sync effect adopted external resets but left the
pending setTimeout in place. When a clear or filter-driven reset arrived
inside the 120ms window, the stale timer would fire after the adopt and
emit the previously-typed query back to the parent, silently undoing the
reset. The skip condition also leaned on lastEmittedRef, which kept a
genuine reset from winning if its value happened to equal the last emit.

Switch the skip to compare the parent value against the locally shown
value (tracked through a ref so the effect deps stay on [value]). On any
external transition the effect now clears the pending timer before
adopting, removing the race entirely. lastEmittedRef is dead under this
model and is removed.

Adds a fake-timer test that types mid-window, rerenders with a different
value before the debounce fires, advances past the original deadline, and
asserts the parent never receives the stale emit.

frontend/src/components/sidebar/__tests__/SidebarSearch.test.tsx

@@ -88,4 +88,35 @@ describe('SidebarSearch', () => {
 
     expect(input.value).toBe('');
   });
+
+  it('cancels the pending debounce emit when the parent resets the value mid-window', () => {
+    const onValueChange = vi.fn();
+    // Start at a non-empty initial so the later reset to '' is a real prop
+    // transition; rerendering with the same string would no-op in React.
+    const { getByPlaceholderText, rerender } = renderInsideCommand({ value: 'initial', onValueChange });
+    const input = getByPlaceholderText('Search stacks...') as HTMLInputElement;
+    expect(input.value).toBe('initial');
+
+    act(() => {
+      fireEvent.input(input, { target: { value: 'web' } });
+    });
+    act(() => {
+      vi.advanceTimersByTime(50);
+    });
+    expect(onValueChange).not.toHaveBeenCalled();
+
+    rerender(
+      <Command shouldFilter={false}>
+        <SidebarSearch value="" onValueChange={onValueChange} />
+      </Command>,
+    );
+
+    act(() => {
+      vi.advanceTimersByTime(200);
+    });
+
+    // The stale timer must not fire and re-emit 'web', undoing the reset.
+    expect(onValueChange).not.toHaveBeenCalled();
+    expect(input.value).toBe('');
+  });
 });