Your first servlet, web.xml and the WAR layout

package com.example.clock;

import jakarta.servlet.annotation.WebServlet;
import jakarta.servlet.http.HttpServlet;
import jakarta.servlet.http.HttpServletRequest;
import jakarta.servlet.http.HttpServletResponse;
import java.io.IOException;
import java.io.PrintWriter;
import java.time.ZoneId;
import java.time.ZonedDateTime;
import java.time.format.DateTimeFormatter;

/** Answers GET requests for /now with the time of day in India. */
@WebServlet("/now")
public class NowServlet extends HttpServlet {
    private static final ZoneId INDIA = ZoneId.of("Asia/Kolkata");
    private static final DateTimeFormatter TIME = DateTimeFormatter.ofPattern("HH:mm:ss");

    @Override
    protected void doGet(HttpServletRequest request, HttpServletResponse response) throws IOException {
        ZonedDateTime now = ZonedDateTime.now(INDIA);
        response.setContentType("text/plain;charset=UTF-8");
        PrintWriter out = response.getWriter();
        out.printf("Time in %s: %s (UTC%s)%n", INDIA, now.format(TIME), now.getOffset());
        out.printf("Answered by the servlet named %s, mapped to %s%n", getServletName(), request.getHttpServletMapping().getPattern());
    }
}

<?xml version="1.0" encoding="UTF-8"?>
<!-- The clock application: one servlet, packaged as a WAR for Tomcat 11. -->
<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 https://maven.apache.org/xsd/maven-4.0.0.xsd">
  <modelVersion>4.0.0</modelVersion>

  <groupId>com.example</groupId>
  <artifactId>clock</artifactId>
  <version>1.0.0</version>
  <!-- war: package builds target/clock.war instead of a JAR. -->
  <packaging>war</packaging>

  <properties>
    <maven.compiler.release>25</maven.compiler.release>
    <project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
  </properties>

  <dependencies>
    <!-- The Servlet 6.1 API to compile against. Scope provided: Tomcat supplies it at run time, so it stays out of
         WEB-INF/lib. -->
    <dependency>
      <groupId>jakarta.servlet</groupId>
      <artifactId>jakarta.servlet-api</artifactId>
      <version>6.1.0</version>
      <scope>provided</scope>
    </dependency>
  </dependencies>

  <build>
    <!-- The WAR's name, and so the application's context path: /clock. -->
    <finalName>clock</finalName>
    <pluginManagement>
      <plugins>
        <plugin>
          <artifactId>maven-clean-plugin</artifactId>
          <version>3.5.0</version>
        </plugin>
        <plugin>
          <artifactId>maven-resources-plugin</artifactId>
          <version>3.5.0</version>
        </plugin>
        <plugin>
          <artifactId>maven-compiler-plugin</artifactId>
          <version>3.16.0</version>
        </plugin>
        <plugin>
          <artifactId>maven-surefire-plugin</artifactId>
          <version>3.6.0</version>
        </plugin>
        <plugin>
          <artifactId>maven-war-plugin</artifactId>
          <version>3.5.1</version>
        </plugin>
        <plugin>
          <artifactId>maven-install-plugin</artifactId>
          <version>3.2.0</version>
        </plugin>
        <plugin>
          <artifactId>maven-deploy-plugin</artifactId>
          <version>3.2.0</version>
        </plugin>
      </plugins>
    </pluginManagement>
  </build>
</project>

<?xml version="1.0" encoding="UTF-8"?>
<!-- The deployment descriptor. Annotations already map NowServlet to /now; this file declares the same class a second
     time, under its own name, and maps that declaration to /ist. -->
<web-app xmlns="https://jakarta.ee/xml/ns/jakartaee"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="https://jakarta.ee/xml/ns/jakartaee https://jakarta.ee/xml/ns/jakartaee/web-app_6_1.xsd"
         version="6.1">
  <servlet>
    <servlet-name>ist-clock</servlet-name>
    <servlet-class>com.example.clock.NowServlet</servlet-class>
  </servlet>
  <servlet-mapping>
    <servlet-name>ist-clock</servlet-name>
    <url-pattern>/ist</url-pattern>
  </servlet-mapping>
</web-app>

from session import run

# Builds the clock WAR with Maven, lists it, deploys it to a fresh Tomcat base on 127.0.0.1:28520 and requests its
# servlet through both mappings, its static page and two files under WEB-INF.
run(
    """
cd clock && mvn -q package
cd clock && jar tf target/clock.war
sh new-base.sh base 28520
cp clock/target/clock.war base/webapps/
$CATALINA_HOME/bin/startup.sh
curl -s http://127.0.0.1:28520/clock/now
curl -s http://127.0.0.1:28520/clock/ist
curl -s -o /dev/null -w "%{http_code} %{content_type}\\n" http://127.0.0.1:28520/clock/
curl -s -o /dev/null -w "%{http_code}\\n" http://127.0.0.1:28520/clock/WEB-INF/web.xml
curl -s -o /dev/null -w "%{http_code}\\n" http://127.0.0.1:28520/clock/WEB-INF/classes/com/example/clock/NowServlet.class
grep -E "Deploying web application archive|has finished" base/logs/catalina.out
$CATALINA_HOME/bin/shutdown.sh
""",
    port=28520,
    show=("java", "maven", "tomcat"),
)

# openjdk version "25.0.4.1" LTS · Apache Maven 3.10.0 · Apache Tomcat 11.0.26
$ cd clock && mvn -q package
$ cd clock && jar tf target/clock.war
META-INF/
META-INF/MANIFEST.MF
WEB-INF/
WEB-INF/classes/
WEB-INF/classes/com/
WEB-INF/classes/com/example/
WEB-INF/classes/com/example/clock/
WEB-INF/classes/com/example/clock/NowServlet.class
WEB-INF/web.xml
index.html
META-INF/maven/com.example/clock/pom.xml
META-INF/maven/com.example/clock/pom.properties
$ sh new-base.sh base 28520
$ cp clock/target/clock.war base/webapps/
$ $CATALINA_HOME/bin/startup.sh
Tomcat started.
$ curl -s http://127.0.0.1:28520/clock/now
Time in Asia/Kolkata: 23:53:00 (UTC+05:30)
Answered by the servlet named com.example.clock.NowServlet, mapped to /now
$ curl -s http://127.0.0.1:28520/clock/ist
Time in Asia/Kolkata: 23:53:00 (UTC+05:30)
Answered by the servlet named ist-clock, mapped to /ist
$ curl -s -o /dev/null -w "%{http_code} %{content_type}\n" http://127.0.0.1:28520/clock/
200 text/html
$ curl -s -o /dev/null -w "%{http_code}\n" http://127.0.0.1:28520/clock/WEB-INF/web.xml
404
$ curl -s -o /dev/null -w "%{http_code}\n" http://127.0.0.1:28520/clock/WEB-INF/classes/com/example/clock/NowServlet.class
404
$ grep -E "Deploying web application archive|has finished" base/logs/catalina.out
… INFO [main] org.apache.catalina.startup.HostConfig.deployWAR Deploying web application archive [base/webapps/clock.war]
… INFO [main] org.apache.catalina.startup.HostConfig.deployWAR Deployment of web application archive [base/webapps/clock.war] has finished in […] ms
$ $CATALINA_HOME/bin/shutdown.sh