Stay with the built-ins
Two windows per screen, halves and quarters, workspaces by hand. Perfectly fine if your work fits in two windows — and the gestures above are already muscle memory for a reason.
Re-read the listCinnamon comes with more window management than most people ever find: halves, quarters, edge snapping, four workspaces. What it does not come with is a layout that stays. Here is the full inventory — and the three ways to go further, with what each one costs.
These are the defaults in Cinnamon 6.x, read from Cinnamon's own keybinding schemas. All of them can be changed under System Settings → Keyboard → Shortcuts → Windows.
The oldest trick on the desktop, and still the fastest for a single window.
Notice the pattern: every gesture moves one window, and the rest of the screen does not react. Neighbours do not make room, and closing a window leaves a hole.
None of this is a bug; Cinnamon's window management simply answers a narrower question than tiling does. What is missing, exactly:
All three are legitimate. They differ in what you keep and what you give up.
Two windows per screen, halves and quarters, workspaces by hand. Perfectly fine if your work fits in two windows — and the gestures above are already muscle memory for a reason.
Re-read the listYou keep the panel, the menu, the themes and the applets, and get layouts on top: presets, auto placement, gaps, rules. This is what greenTile does, and gTile is the other option in the catalogue.
Compare the extensions →i3, sway, bspwm and friends tile by nature and are loved for it. The cost is real: you log into a different session, and Cinnamon's panel, applets and menu do not come with it. Choose it at the login screen, not instead of Cinnamon.
i3 on GitHubThe install is a zip and a script, and it does not touch the rest of your desktop:
./install.sh, restart Cinnamon (CtrlAltEsc), then enable greenTile in the Extensions manager.