Ask one question about whether background effects can run

- The menu asked the browser; the pipeline asked the browser and for a
  desktop. On a phone whose browser can run them, blur was offered and
  then refused: the toggle moved and the video did not change.
- Both now ask one function, and it asks the browser alone. The platform
  was the wrong measure: a phone on the fast route held 99% of its frame
  rate and was refused, a desktop on the slow one held 73% and was
  allowed.
- The in-call device switcher is still withheld on a phone; that is the
  device menu's own rule and is unchanged.
- The provider tests run as a phone, and fail with the desktop test back.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

src/livekit/backgroundProcessing.ts

@@ -0,0 +1,16 @@
+/*
+Copyright 2026 Element Creations Ltd.
+
+SPDX-License-Identifier: AGPL-3.0-only OR LicenseRef-Element-Commercial
+Please see LICENSE in the repository root for full details.
+*/
+
+import { supportsBackgroundProcessors as supportsBackgroundProcessorsLivekitSdk } from "@livekit/track-processors";
+
+/**
+ * Whether this browser can run background effects: the one answer for the
+ * controls and the pipeline, so nothing is offered that the pipeline refuses.
+ */
+export function supportsBackgroundProcessors(): boolean {
+  return supportsBackgroundProcessorsLivekitSdk();
+}