If you cannot drag the Finder thumbnail or group Finder with other windows in Stage Manager, it is almost always because Finder is set to "All Desktops". When an app is configured to appear across all spaces, macOS locks it out of Stage Manager's auto-hide and custom app-set grouping behavior.
How to Fix It:
Check the Finder Dock Options:
- Open Finder so its icon is active in the Dock.
- Control-click (or right-click) the Finder icon in the Dock.
- Look under Options.
- If Assign to: All Desktops is checked, change it to None (or This Desktop).
- (Note: The "All Desktops" option only appears if you currently have more than one Desktop/Space active via Mission Control).
Relaunch Finder (if needed):
- Press and hold the Option key, then right-click the Finder icon in the Dock and select Relaunch, or use the Apple menu to Force Quit and relaunch Finder.
Group Finder in Stage Manager:
- Once Finder is unlinked from "All Desktops," it will appear properly in the recent apps strip on the left.
- You can now drag its thumbnail into your active workspace or use Shift-click to combine Finder windows with your current group of apps.
More info from Apple: Work in multiple spaces on Mac - Apple Support