The word is borrowed from tiling window managers, and the borrowing is exact: a pane is a rectangle showing one thing, arranged next to other rectangles rather than stacked behind them.
What makes it different from an editor tab is what sits behind it. An inactive editor tab is a string in memory. An inactive pane may be a shell with a running process, a browser with a page, or an agent mid-turn.
The cost nobody budgets for
Panes are not free while hidden. A terminal emulator keeps redrawing. A browser keeps running timers and animations. A chat keeps a socket open and re-renders on every streamed token. Ten panes on screen is a layout problem; ten panes alive is a performance problem, and it is the one that shows up as a laptop fan.
There are two honest answers and you need both. Cap how many panes stay resident at once, and freeze the ones nobody is looking at: stop their timers, stop their repaints, keep their state.
Hidden is not the same as unfocused
The trap is deciding what "nobody is looking at" means. Window focus is the tempting signal and it is the wrong one: a pane in a background window that the user is watching while typing elsewhere is very much being looked at, and freezing it makes the app feel broken in a way that is hard to report.
Visibility (is this rectangle actually on screen) is the signal that survives contact with how people really work.
Freezing hidden panes measured a 23-28% reduction in CPU at rest. The liveness gate is deliberately built on visibility and never on window focus.