Не получается открыть сервлет с помощью tomcat

Начал изучать сервлеты, пишу в VSCode, застрял на моменте создания варника и запуска на Tomcat. Помогите найти ошибки в коде.

pom.xml

<?xml version="1.0" encoding="UTF-8"?>

<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
  xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
  <modelVersion>4.0.0</modelVersion>

  <groupId>com.example</groupId>
  <artifactId>demo</artifactId>
  <version>1.0-SNAPSHOT</version>
  <packaging>war</packaging>

  <name>demo Maven Webapp</name>
  
  <url>http://localhost</url>

  <properties>
    <project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
    <maven.compiler.source>1.7</maven.compiler.source>
    <maven.compiler.target>1.7</maven.compiler.target>
  </properties>

  <dependencies>
    <dependency>
      <groupId>javax.servlet</groupId>
      <artifactId>javax.servlet-api</artifactId>
      <version>4.0.1</version>
  </dependency>
    <dependency>
      <groupId>junit</groupId>
      <artifactId>junit</artifactId>
      <version>4.11</version>
      <scope>test</scope>
    </dependency>
  </dependencies>

  <build>
    <finalName>demo</finalName>
    <pluginManagement><!-- lock down plugins versions to avoid using Maven defaults (may be moved to parent pom) -->
      <plugins>
        <plugin>
          <artifactId>maven-war-plugin</artifactId>
          <configuration>
              <attachClasses>true</attachClasses>
              <webXml>target/web.xml</webXml>
              <webResources>
                  <resource>
                      <directory>src/main/webapp</directory>
                      <filtering>true</filtering>
                  </resource>
              </webResources>
          </configuration>
      </plugin>
        <plugin>
          <artifactId>maven-clean-plugin</artifactId>
          <version>3.1.0</version>
        </plugin>
        <!-- see http://maven.apache.org/ref/current/maven-core/default-bindings.html#Plugin_bindings_for_war_packaging -->
        <plugin>
          <artifactId>maven-resources-plugin</artifactId>
          <version>3.0.2</version>
        </plugin>
        <plugin>
          <artifactId>maven-compiler-plugin</artifactId>
          <version>3.8.0</version>
          <configuration>
            <fork>true</fork>
            <executable>C:\Program Files\Java\jdk-17\bin</executable>
            </configuration>
        </plugin>
        <plugin>
          <artifactId>maven-surefire-plugin</artifactId>
          <version>2.22.1</version>
        </plugin>
        <!-- <plugin>
          <artifactId>maven-war-plugin</artifactId>
          <version>3.2.2</version>
        </plugin> -->
        <plugin>
          <artifactId>maven-install-plugin</artifactId>
          <version>2.5.2</version>
        </plugin>
        <plugin>
          <artifactId>maven-deploy-plugin</artifactId>
          <version>2.8.2</version>
        </plugin>
      </plugins>
    </pluginManagement>
  </build>
</project>

Класс сервлета:

 package com.example;
 
import javax.servlet.ServletException;
import javax.servlet.annotation.WebServlet;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import java.io.IOException;
import java.io.PrintWriter;
 
@WebServlet("/api")
public class servletTest extends HttpServlet {
 
   @Override
   protected void doGet(HttpServletRequest req, HttpServletResponse resp) throws ServletException, IOException {
       resp.setContentType("text/html");
       PrintWriter printWriter = resp.getWriter();
       printWriter.write("Hello!");
       printWriter.close();
   }
}

web.xml

    <!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>servletTest</servlet-name>
    <servlet-class>com.example.servletTest</servlet-class>
  </servlet>
  <servlet-mapping>
    <servlet-name>servletTest</servlet-name>
    <url-pattern>/api</url-pattern>
  </servlet-mapping>
</web-app>

index.jsp

<html>
<body>
<h2>Hello World!</h2>
</body>
</html>