gnome-shell-extension-simulate-switching-workspaces-on-active-monitor

(almost) allows to have separate workspaces on multiple monitors

Details

After you switch to a different workspace(by using the preview, or by selecting an app on the dock), the windows on the monitors that don't have the focus are moved to the visible workspace.
So it looks like you are switching workspaces only on the active monitor, leaving the others unchanged.

Prerequisites

• The option "Workspaces span displays" from tweaks must be active.
• The option "Static Workspaces" must be active.

Hot keys

• Ctrl+Alt+q Switch to the previous workspace on the active monitor
• Ctrl+Alt+a Switch to the next workspace on the active monitor

Development

In order to develop npm (v9 or later) must be installed.
IMPORTANT: All the following commands must be executed in the simulate-switching-workspaces-on-active-monitor@micheledaros.com directory.

• Install the dependencies: npm i
• Build the extension: npm run build
• Install the extension (will also build it): npm run install
  • After installing the extension, Gnome needs to be restarted/run nested. For that, please follow the steps in the official guide.

GNOME 45 notes

Some of the APIs required for this extension are now gone. Because of this, the extension can no longer easily know what is the currently focused window, and now assumes your mouse pointer is on the monitor you want to switch.