@salesforce/community/basePath gives us the Experience Cloud Site URL. We can append /secur/logout.jsp to develop Logout Link using Salesforce Lightning Web Component for Experience Cloud Users.

Lightning Web Component:

HTML:

<template>
	<template if:false={isGuest}>
        Logout URL is {logoutUrl}<br/><br/>
		<a href={logoutUrl}>Logout</a>
	</template>
</template>

JavaScript:

import { LightningElement } from 'lwc';
import isGuest from "@salesforce/user/isGuest";
import basePath from "@salesforce/community/basePath";

export default class LogoutLink extends LightningElement {

    get isGuest() {
        return isGuest;
    }

    get logoutUrl() {
        
        const sitePrefix = basePath.replace(
            /\/s$/i, ""
        ); 
        return sitePrefix + "/secur/logout.jsp";

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>59.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightningCommunity__Page</target>
    </targets>
</LightningComponentBundle>

Output: