For securing Tomcat from hackers, it's recommended that we try a few steps at hiding the tomcat version information. The OWASP project suggests a few steps. https://www.owasp.org/index.php/Securing_tomcat . If a tomcat installation is thus protected, then only 1 of the above answers will show the version of tomcat.
i.e going through the $TOMCAT_HOME\RELEASE-NOTES file where the version number is clearly announced.
I had one such protected server and only the RELEASE-NOTES file revealed the version of the tomcat. all other techniques failed to reveal the version info.