I accidentally discovered a new-to-me feature in Sakura (also in Konsole). If I hit F11, I'll get a truly full screen version of the console ... while still having the extra benefits that come with running it in a GUI as opposed to a virtual terminal.
(Example things that work better from the GUI side: changing font size, better color support, better mouse integration.)
On others like LibreOffice it opens a sidebar, so it's the "surprise me" key I guess!