Chromium session management on X11 vs Wayland

I use a chromium based web browser (brave) on awesome-wm (WM for X11). My normal workflow is to have 1 or 2 brave windows open on each virtual desktop. Then I would click the hamburger icon (settings) and click "Exit". This would close all my brave windows in all my virtual desktops. Then, if I was to launch brave, it would remember the exact mapping between the windows and to which virtual desktops those windows belong in. Hence, brave would place the windows in their respective virtual desktops. However in Wayland, if I was to do the same thing (be it sway or hyprland), brave would open ALL the windows in the same desktop. I am under the impression that session management in this context would be a delegation of the application (brave). I also tried google chrome, but it behaves exactly like brave. I also had a similar workflow on KDE (with X11), and things worked well there. Is there a workaround, maybe some chromium extension to make things work here? Also, is this really an issue in brave/chromium or is it an issue in wayland not implementing the session managemnt of chromium? Thank you