Fix incorrect label for background sessions in Agent Sessions status bar

Co-authored-by: bpasero <900690+bpasero@users.noreply.github.com>

Author: Copilot

src/vs/workbench/contrib/chat/browser/chatSessions/chatSessions.contribution.ts

@@ -44,6 +44,7 @@ import { IMarkdownString } from '../../../../../base/common/htmlContent.js';
 import { IViewsService } from '../../../../services/views/common/viewsService.js';
 import { ChatViewId } from '../chat.js';
 import { ChatViewPane } from '../widgetHosts/viewPane/chatViewPane.js';
+import { AgentSessionProviders } from '../agentSessions/agentSessions.js';
 
 const extensionPoint = ExtensionsRegistry.registerExtensionPoint<IChatSessionsExtensionPoint[]>({
 	extensionPoint: 'chatSessions',
@@ -331,8 +332,12 @@ export class ChatSessionsService extends Disposable implements IChatSessionsServ
 	public reportInProgress(chatSessionType: string, count: number): void {
 		let displayName: string | undefined;
 
-		if (chatSessionType === localChatSessionType) {
-			displayName = 'Local Chat Agent';
+		if (chatSessionType === AgentSessionProviders.Local) {
+			displayName = localize('chat.session.inProgress.local', "Local Agent");
+		} else if (chatSessionType === AgentSessionProviders.Background) {
+			displayName = localize('chat.session.inProgress.background', "Background Agent");
+		} else if (chatSessionType === AgentSessionProviders.Cloud) {
+			displayName = localize('chat.session.inProgress.cloud', "Cloud Agent");
 		} else {
 			displayName = this._contributions.get(chatSessionType)?.contribution.displayName;
 		}