Minimize PWA to System Tray

It would be nice to be able to minimize Progressive Web App windows to the System Tray. Sometimes I use PWA to keep messaging and collaboration apps open (such as MS Teams, Google Chat etc.). It would like to have their icons always visible on the screen, possibly flashing in some way if there is a notification, when I use any maximized application. I would like to avoid to clutter my OS taskbar with PWA windows, because I use old style uncombined task buttons with icon and title.