Keep background effects to desktops until the menu says what they cost

- The one support check asks for a desktop again, as #4059 had the
  pipeline do: menu and pipeline still agree, so a phone is neither
  offered blur nor refused it.
- Lifting it moves to the PR that tells the user where effects run
  slowly, so it is their choice to make.

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

src/components/CallFooterViewModel.test.ts

@@ -243,9 +243,9 @@ describe("createCallFooterViewModel", () => {
       );
     }
 
-    it("offers them on a phone whose browser can run them", () => {
+    it("offers nothing on a phone, where the pipeline would refuse them", () => {
       sdkSupportMock.mockReturnValue(true);
-      expect(lobbyOn("ios").toggleBlur$.value).toBeDefined();
+      expect(lobbyOn("ios").toggleBlur$.value).toBeUndefined();
     });
 
     it("offers them where the pipeline will honour them", () => {

src/livekit/TrackProcessorContext.test.ts

@@ -48,8 +48,8 @@ vi.mock("@livekit/track-processors", () => ({
   }),
   supportsBackgroundProcessors: (): boolean => true,
 }));
-// A phone: the pipeline must not ask.
-vi.mock("../Platform", () => ({ platform: "ios" }));
+const platformMock = vi.hoisted(() => ({ platform: "desktop" }));
+vi.mock("../Platform", () => platformMock);
 vi.mock("./BackgroundEffectTransformer", () => ({
   BackgroundEffectTransformer: vi.fn(),
 }));
@@ -176,6 +176,7 @@ describe("ProcessorProvider", () => {
     pipelines.built = 0;
     pipelines.destroyed = 0;
     pipelines.switches = [];
+    platformMock.platform = "desktop";
     backgroundBlur.setValue(false);
   });
   afterEach(() => backgroundBlur.setValue(false));
@@ -194,13 +195,14 @@ describe("ProcessorProvider", () => {
     expect(track.stopProcessor).not.toHaveBeenCalled();
   });
 
-  it("runs on a phone whose browser can run it", async () => {
+  it("does not run on a phone, even where its browser could", async () => {
+    platformMock.platform = "ios";
     const track = cameraTrack();
     render(surfaces(track));
     await blur(true);
 
-    expect(latest().supported).toBe(true);
-    expect(track.setProcessor).toHaveBeenCalledWith(latest().processor);
+    expect(latest().supported).toBe(false);
+    expect(track.setProcessor).not.toHaveBeenCalled();
   });
 
   it("preview and call share one pipeline", async () => {

src/livekit/backgroundProcessing.ts

@@ -7,10 +7,9 @@ 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.
- */
+import { platform } from "../Platform";
+
+/** One answer for the controls and the pipeline, so neither offers what the other refuses. */
 export function supportsBackgroundProcessors(): boolean {
-  return supportsBackgroundProcessorsLivekitSdk();
+  return supportsBackgroundProcessorsLivekitSdk() && platform === "desktop";
 }