Name the background effect pieces after background effects

- One name, as review asked: TrackProcessorContext becomes
  BackgroundEffectsContext, with BackgroundEffectsProvider,
  BackgroundEffectsState, useBackgroundEffects,
  useBackgroundEffectsState$ and useSyncBackgroundEffects.
- The state's Behavior is backgroundEffectsState$ wherever it is passed,
  in place of trackProcessorState$, trackerProcessorState$ and
  processorState$.
- Renames only: nothing changes in behaviour.

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

src/room/LobbyView.tsx

@@ -40,9 +40,9 @@ import { useMediaDevices } from "../MediaDevicesContext";
 import { ObservableScope } from "../state/ObservableScope";
 import { useInitial } from "../useInitial";
 import {
-  useTrackProcessor,
-  useTrackProcessorSync,
-} from "../livekit/TrackProcessorContext";
+  useBackgroundEffects,
+  useSyncBackgroundEffects,
+} from "../livekit/BackgroundEffectsContext";
 import { getValue } from "../utils/observable";
 import { useBehavior } from "../useBehavior";
 import { CallFooter, type FooterSnapshot } from "../components/CallFooter";
@@ -136,7 +136,7 @@ export const LobbyView: FC<Props> = ({
       },
   );
 
-  const { processor } = useTrackProcessor();
+  const { processor } = useBackgroundEffects();
 
   const initialProcessor = useInitial(() => processor);
   const localTrackOptions = useMemo<CreateLocalTracksOptions>(
@@ -183,7 +183,7 @@ export const LobbyView: FC<Props> = ({
     }
   }, [devices, videoInputId, videoTrack]);
 
-  useTrackProcessorSync(videoTrack);
+  useSyncBackgroundEffects(videoTrack);
 
   const [footerVm, setFooterVm] = useState<ViewModel<FooterSnapshot> | null>(
     null,