I think this would make it a lot easier to use the feature. Having to move my hand to my mouse (or trackpad) to toggle this makes it just that much more likely I’m going to go to Perplexity to search instead (since I have a keyboard shortcut for this).
If it would be simpler, this could be implemented as something in the menu bar, and then we can configure the shortcut in System Settings > Keyboard > Keyboard Shortcuts > App Shortcuts.
Thank you for considering this request!