The red notifications are the todos to check later. Don't treat them as interruptions, treat them as something to check when you have time. Or simply turn Slack off when you are busy.
It may also be worth noting that if you personally feel anxiety due to this, that is not a universal feeling. It is a legitimate feeling, and does need a resolution, but it is more likely something you'd want to individually work on via various coping skills. If that process is new to you, I recommend at least a short-term therapist to teach you some of the basics for dealing with and adapting to anxiety triggers.
In the same menu, you could also choose to set yourself as "Away".