way to overlap Teams interface to run a custom web app

my goal is to have a persistent web app running alongside and within Teams, that does not get killed everytime the user goes to another part of Teams, as it happens to tab apps

is there a way for me to generate something like a sticky pop up window overlapping Teams interface, just like it happens when you're on an active call for example and goes to the "Chat" tab?

if not, is there some other alternative of some sort that I can use to achieve my goal?