At the moment, STS4 doesn't have all the bits and pieces pre-installed to deploy apps from within the IDE to local Tomcat servers. The current version of the tooling is focused on running Spring Boot applications in the embedded Tomcat mode.
Having said that, we are working on this, the next update will come with the necessary extensions pre-installed to deploy war-packaged Boot apps to a local Tomcat directly.
If you want to give it a try, feel free to grab one of the latest nightly builds of STS 4.1.1, anything post B1473 should include the necessary pieces. If not, please file a bug at https://github.com/spring-projects/sts4/issues to get that fixed.
If you want to fix an existing STS4 installation, you would need to add the m2e-wtp integration extensions, which you should be able to find on the main Eclipse update site of your installation. Go to "Install New Software", select the main Eclipse update site, and search for "m2e-wtp".