According to Applications Manager compatibility matrix found here, Tomcat 10 is the highest version listed as compatible with Applications Manager.
Will Tomcat 11 work with Applications Manager?
Cause
Tomcat 11 requires Java 17 Applications Manager is compatible with Java 17 from version 9.5 to 9.5.3
Resolution
Applications Manager is compatible with Tomcat 11 in the following configuration:
Application Manager's master/local Agent where Tomcat is likely installed is running Java/OpenJDK 17.
Applications Manager version must be 9.5, 9.5.1, 9.5.2, or 9.5.3 (9.4.x and below does not support Java 17 and 9.6+ includes its own integrated web server)