Using Service Cloud Voice LWC Toolkit API Events, we can perform actions using Lightning Web Component.

Sample Code:

HTML:

<template>
    <lightning-service-cloud-voice-toolkit-api>        
    </lightning-service-cloud-voice-toolkit-api>
</template>

JavaScript:

import { LightningElement } from 'lwc';

export default class VoiceCallListener extends LightningElement {

    callEndedListener;
    callConnectedListener;

    constructor() {

        console.log( 'Inside the Constructor' );
        super();
        this.callConnectedListener = this.onCallConnected.bind( this );
        this.callEndedListener = this.onCallEnded.bind( this );

    }    

    renderedCallback() {

        console.log( 'Inside Connected Callback' );
        const toolkitApi = this.template.querySelector( 
            'lightning-service-cloud-voice-toolkit-api' 
        );
        if( toolkitApi ) {

            console.log( 'Inside Toolkit API' );
            toolkitApi.addEventListener( 'callconnected', this.callConnectedListener );           
            toolkitApi.addEventListener( 'callended', this.callEndedListener );

        }

    }

    onCallConnected( event ) {        

        console.log( 'Call Connected Voice Toolkit event detail is', JSON.stringify( event.detail ) );
        
    }

    onCallEnded( event ) {        

        console.log( 'Call Ended Voice Toolkit event detail is', JSON.stringify( event.detail ) );
        
    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>55.0</apiVersion>
    <isExposed>true</isExposed>  
    <capabilities>
        <capability>lightning__ServiceCloudVoiceToolkitApi</capability>
    </capabilities>
    <targets>
        <target>lightning__UtilityBar</target>
    </targets>
</LightningComponentBundle>

Lightning App Configuration:

Output: