Make the type of participant$ stricter

It is, in fact, required to be a behavior.

src/state/MediaViewModel.ts

@@ -259,7 +259,7 @@ abstract class BaseMediaViewModel {
     public readonly userId: string,
     // We don't necessarily have a participant if a user connects via MatrixRTC but not (yet) through
     // livekit.
-    protected readonly participant$: Observable<
+    protected readonly participant$: Behavior<
       LocalParticipant | RemoteParticipant | null
     >,
 
@@ -410,7 +410,7 @@ abstract class BaseUserMediaViewModel extends BaseMediaViewModel {
      * The expected identity of the LiveKit participant. Exposed for debugging.
      */
     public readonly rtcBackendIdentity: string,
-    participant$: Observable<LocalParticipant | RemoteParticipant | null>,
+    participant$: Behavior<LocalParticipant | RemoteParticipant | null>,
     encryptionSystem: EncryptionSystem,
     livekitRoom$: Behavior<LivekitRoom | undefined>,
     focusUrl$: Behavior<string | undefined>,
@@ -678,7 +678,7 @@ export class RemoteUserMediaViewModel extends BaseUserMediaViewModel {
     id: string,
     userId: string,
     rtcBackendIdentity: string,
-    participant$: Observable<RemoteParticipant | null>,
+    participant$: Behavior<RemoteParticipant | null>,
     encryptionSystem: EncryptionSystem,
     livekitRoom$: Behavior<LivekitRoom | undefined>,
     focusUrl$: Behavior<string | undefined>,
@@ -780,7 +780,7 @@ export class ScreenShareViewModel extends BaseMediaViewModel {
     scope: ObservableScope,
     id: string,
     userId: string,
-    participant$: Observable<LocalParticipant | RemoteParticipant>,
+    participant$: Behavior<LocalParticipant | RemoteParticipant>,
     encryptionSystem: EncryptionSystem,
     livekitRoom$: Behavior<LivekitRoom | undefined>,
     focusUrl$: Behavior<string | undefined>,

src/state/ScreenShare.ts

@@ -4,7 +4,7 @@ Copyright 2025 New Vector Ltd.
 SPDX-License-Identifier: AGPL-3.0-only OR LicenseRef-Element-Commercial
 Please see LICENSE in the repository root for full details.
 */
-import { of } from "rxjs";
+
 import {
   type LocalParticipant,
   type RemoteParticipant,
@@ -14,7 +14,7 @@ import {
 import { type ObservableScope } from "./ObservableScope.ts";
 import { ScreenShareViewModel } from "./MediaViewModel.ts";
 import type { EncryptionSystem } from "../e2ee/sharedKeyManagement.ts";
-import type { Behavior } from "./Behavior.ts";
+import { constant, type Behavior } from "./Behavior.ts";
 
 /**
  * A screen share media item to be presented in a tile. This is a thin wrapper
@@ -40,7 +40,7 @@ export class ScreenShare {
       this.scope,
       id,
       userId,
-      of(participant),
+      constant(participant),
       encryptionSystem,
       livekitRoom$,
       focusUrl$,