Não segura o tema na troca de páginas | Java e JSF 2 - II: Componentes ricos com Primefaces

Eu fiz o que o exercício pediu, mas ainda ele não segura o tema quando troco a página. Faltou algo?

package br.com.caelum.livraria.bean;

import javax.faces.bean.ManagedBean;
import javax.faces.bean.SessionScoped;

@ManagedBean
@SessionScoped
public class TemaBean {

    private String tema = "vader";

    public String getTema() {
        return tema;
    }

    public void setTema(String tema) {
        this.tema = tema;
    }
}

<?xml version="1.0" encoding="UTF-8" ?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"
    xmlns:h="http://xmlns.jcp.org/jsf/html"
    xmlns:f="http://xmlns.jcp.org/jsf/core"
    xmlns:p="http://primefaces.org/ui"
    xmlns:ui="http://xmlns.jcp.org/jsf/facelets">

    <h:head/>
    <h:body>
        <div id="cabecalho">
            <h:graphicImage library="img" name="logo.png"/>

            <h:form>
                <p:themeSwitcher id="basic" style="width:165px" value="#{temaBean.tema}">
                    <f:selectItem itemLabel="Choose Theme" itemValue="" />
                    <f:selectItem itemLabel="Aristo" itemValue="aristo" />
                    <f:selectItem itemLabel="Vader" itemValue="vader" />
                    <f:ajax />
                </p:themeSwitcher>
             </h:form>

               <p:growl id="growl" showDetail="true" autoUpdate="true" sticky="true"/>

            <h:form rendered="#{usuarioLogado != null}">

                <p:menuButton value="Menu">
                    <p:menuitem value="Livros" action="livro?faces-redirect=true" icon="fa fa-fw fa-edit"/>
                    <p:menuitem value="Autores" action="autor?faces-redirect=true" icon="fa fa-fw fa-edit"/>
                    <p:separator />
                    <p:menuitem value="Logout" action="#{loginBean.deslogar}" icon="fa fa-fw fa-sign-out"/>
                </p:menuButton>
            </h:form>

            <h1><ui:insert name="titulo"></ui:insert></h1>
        </div>
        <div id="conteudo">
            <ui:insert name="conteudo">
            </ui:insert>
        </div>
        <div id="rodape">
            Copyright 2018
            <ui:insert name="texto">
            </ui:insert>
            <br />
            <h:outputText value="Usuário logado: #{sessionScope['usuarioLogado'].email}"/>
        </div>
    </h:body>
</html>