Browsers are tinkering with ways to display multiple web apps at once: An AI chatbot in a sidebar or "workspaces".
A more flexible solution that allows you to mix and match windows as you please are tiling window managers like Sway for Linux or Amethyst for macOS. They support many virtual desktops first-class options for supporting windows side-by-side.
https://swaywm.org/
https://ianyh.com/amethyst/
Shouldn't need different ways to switch normal apps & web-apps within a browser.