新泽西的Rest API:我缺少什么?

我有一个正在工作的ServletMaven项目,我想用一个基于Jersey的Restapi来扩展它。

import javax.ws.rs.GET;
import javax.ws.rs.Path;
import javax.ws.rs.Produces;
import javax.ws.rs.core.MediaType;

@Path("/api")
public class CheckHaveIBeenPwned {

    @GET
    @Produces( "text/html;charset=UTF-8" )
    public String whatever() {
        return "Hallo";
    }

}

在pom.xml中,我包含了以下jersey依赖项:

<dependency>
  <groupId>com.sun.jersey</groupId>
  <artifactId>jersey-core</artifactId>
  <version>1.19.1</version>
</dependency>
<dependency>
  <groupId>com.sun.jersey</groupId>
  <artifactId>jersey-client</artifactId>
  <version>1.19.1</version>
</dependency>
<dependency>
  <groupId>com.sun.jersey</groupId>
  <artifactId>jersey-server</artifactId>
  <version>1.19.1</version>
</dependency>
<dependency>
  <groupId>com.sun.jersey</groupId>
  <artifactId>jersey-json</artifactId>
  <version>1.19.1</version>
</dependency>

我的web.xml(本质上)如下所示:

<!DOCTYPE web-app PUBLIC "-//Sun Microsystems, Inc.//DTD Web Application 2.3//EN" "http://java.sun.com/dtd/web-app_2_3.dtd" >

<web-app>
  <display-name>Archetype Created Web Application</display-name>
  <servlet>
    <servlet-name>ExistingServletClass</servlet-name>
    <servlet-class>com.whatever.servlet.ExistingServletClass</servlet-class>
  </servlet>
  <!-- a few more (still working) servlet sections -->
  <servlet>
      <display-name>JAX-RS REST Servlet</display-name>
      <servlet-name>REST-Servlet</servlet-name>
      <servlet-class>com.sun.jersey.spi.container.servlet.ServletContainer</servlet-class>
      <init-param>
          <param-name>com.sun.jersey.api.json.POJOMappingFeature</param-name>
          <param-value>true</param-value>
      </init-param>
      <load-on-startup>1</load-on-startup>
  </servlet>

  <servlet-mapping>
      <servlet-name>REST-Servlet</servlet-name>
      <url-pattern>/rest/*</url-pattern>
  </servlet-mapping>
  <servlet-mapping>
    <servlet-name>ExistingServletClass</servlet-name>
    <url-pattern>/existingservletclass</url-pattern>
  </servlet-mapping>
  <-- a few more (still working) servlet mappings -->
  <welcome-file-list>
    <welcome-file>index.jsp</welcome-file>
  </welcome-file-list>
</web-app>

但当我尝试调用API时(只需在浏览器中打开以下URL):

https://my.url:8443/myapp/rest/api

https://my.url:8443/myapp

我错过了什么?我在另一个项目中做了一件非常相似的事情,并且成功了。但是,将Rest API添加到现有项目中会一直失败。。。