Change:
import { RunOnceScheduler } from 'vs/base/common/async'; import { Disposable, IDisposable } from 'vs/base/common/lifecycle'; import { AudioCue, IAudioCueService } from 'vs/platform/audioCues/browser/audioCueService'; <ins> import { IInstantiationService } from 'vs/platform/instantiation/common/instantiation'; </ins> import { IChatAccessibilityService } from 'vs/workbench/contrib/chat/browser/chat'; import { IChatResponseViewModel } from 'vs/workbench/contrib/chat/common/chatViewModel'; <del> const CHAT_RESPONSE_PENDING_AUDIO_CUE_LOOP_MS = 5000; const CHAT_RESPONSE_PENDING_ALLOWANCE_MS = 4000; </del> export class ChatAccessibilityService extends Disposable implements IChatAccessibilityService { declare readonly _serviceBrand: undefined; <del> private _pendingCueMap: Map<number, IDisposable | undefined> = new Map(); </del> <ins> private _pendingCueMap: Map<number, AudioCueScheduler> = new Map(); </ins> <del> private _runOnceScheduler: RunOnceScheduler; private _lastResponse: string | undefined; </del> private _requestId: number = 0; <del> constructor(@IAudioCueService private readonly _audioCueService: IAudioCueService) { </del> <ins> constructor(@IAudioCueService private readonly _audioCueService: IAudioCueService, @IInstantiationService private readonly _instantiationService: IInstantiationService) { </ins> super(); <del> this._register(this._runOnceScheduler = new RunOnceScheduler(() => { this._pendingCueMap.set(this._requestId, this._audioCueService.playAudioCueLoop(AudioCue.chatResponsePending, CHAT_RESPONSE_PENDING_AUDIO_CUE_LOOP_MS)); }, CHAT_RESPONSE_PENDING_ALLOWANCE_MS)); </del> } acceptRequest(): number { this._requestId++; this._audioCueService.playAudioCue(AudioCue.chatRequestSent, { allowManyInParallel: true }); <del> this._runOnceScheduler.schedule(); </del> <ins> this._pendingCueMap.set(this._requestId, this._register(this._instantiationService.createInstance(AudioCueScheduler))); </ins> return this._requestId; } acceptResponse(response: IChatResponseViewModel | string | undefined, requestId: number): void { this._pendingCueMap.get(requestId)?.dispose(); this._pendingCueMap.delete(requestId); const isPanelChat = typeof response !== 'string'; <del> this._runOnceScheduler?.cancel(); </del> const responseContent = typeof response === 'string' ? response : response?.response.asString(); <del> if (this._lastResponse === responseContent) { return; } </del> this._audioCueService.playAudioCue(AudioCue.chatResponseReceived, { allowManyInParallel: true }); if (!response) { return; } const errorDetails = isPanelChat && response.errorDetails ? ` ${response.errorDetails.message}` : ''; <del> this._lastResponse = responseContent; </del> status(responseContent + errorDetails); } } <ins> const CHAT_RESPONSE_PENDING_AUDIO_CUE_LOOP_MS = 5000; const CHAT_RESPONSE_PENDING_ALLOWANCE_MS = 4000; /** * Schedules an audio cue to play when a chat response is pending for too long. */ class AudioCueScheduler extends Disposable { private _scheduler: RunOnceScheduler; private _audioCueLoop: IDisposable | undefined; constructor(@IAudioCueService private readonly _audioCueService: IAudioCueService) { super(); this._scheduler = new RunOnceScheduler(() => { this._audioCueLoop = this._audioCueService.playAudioCueLoop(AudioCue.chatResponsePending, CHAT_RESPONSE_PENDING_AUDIO_CUE_LOOP_MS); }, CHAT_RESPONSE_PENDING_ALLOWANCE_MS); this._scheduler.schedule(); } override dispose(): void { super.dispose(); this._audioCueLoop?.dispose(); this._scheduler.cancel(); this._scheduler.dispose(); } } </ins>

Discussion:
The lastResponse property is checked before unsetting the hasReceivedRequest_ field
This won't happen if happens
AFAIK this will still happen: when having two equal responses (which is the default for inline chat), is only played once.