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Mosaic is an i3-style auto-tiling extension for GNOME Shell
Mosaic brings i3-style automatic tiling to GNOME Shell without asking you to choose it permanently. Turn it on when you want windows to arrange themselves, turn it off when you want floating windows back.
The extension works with GNOME 45 and up, adding a toggle to Quick Settings to enable the auto-tiling mode. When off, you’re in floating mode (which still has tiling features). Expand the toggle to access more options or get at Mosaic’s settings.
It’s the on-demand nature that makes Mosaic more interesting as a tool.
When the auto-tiling mode is active (the toggle is turned on) all your windows tile for you the moment you open them, using a tree-based i3-style approach, per the Mosaic GitHub.
Naturally, there are plenty of keyboard shortcuts to manipulate and manage windows on your workspace.
Press super + return to enter window management mode then:
Outside of window management mode, press super + g to toggle a window between floating and tiled state, and press super + r to enable the resize mode. You can use your mouse to drag between gaps (gap size configurable in settings) to resize too.
Window management mode works when auto-tiling is off, albeit a little different – useful if you want to create a more exotic arrangement of apps using your keyboard.
I did, however, notice less fluidity when moving floating windows when this extension was installed and enabled, but auto-tiling was off. Your mileage may vary.
If all of this reminds you of System76’s Pop Shell, there is a good reason: Mosaic began as a fork of it. Pop!_OS has since moved from GNOME Shell to the COSMIC desktop, where similar functionality comes built into the desktop.