What's heavy about any of that? I don't know what Tomcat is, but Docker is just a means of installing and running software in a VM(if host isn't Linux), Java is a perfectly fine language and runtime, and Postgres is a powerful and widely-used database. Any other self-hosted web app would require at least a language runtime and a database.
I currently use taskwarrior and nextcloud to synchronize task states between computers. This web based solution would help get rid of the synchronization part if it replicated enough of taskwarrior's functionality.
What I use most in taskwarrior is creating, starting, stopping and closing tasks under projects, then I use hooks written in python which read the changes from stdin and post the task changes to jira and slack.
So if this project could support web hooks, I could write a glue service for it to call when new tasks are created or states are changed.
I love the UI! Maybe this would get into the hands of more people if it were just statically hosted html + js (maybe on gh-pages) that stored your todo items in browser local storage?