I will just share a somewhat similar project: https://github.com/netflix/dispatch Also open source, also Python, also incident management, also custom severities (but not as much of custom roles, afaik) :) Has some integrations with slack, but not focused on Slack particularly. Can be a good project to learn from as well :) My relation to it: I only contributed with a couple of pull requests there :)
https://bestpractical.com/rtir
I haven't used their Incident Response but used the basic RT for years. It's solid and never gave us any trouble. It is all (or mostly) written in Perl however if that is a concern.
Open-source and free to run on your own, or you can pay for cloud hosting and support.