On macOS the standard shortcut for switching the keyboard layout is Cmd+Space. Also, in general, most shortcuts use Cmd instead of Ctrl. However, zathura seems to ignore Cmd completely. Therefore, there are two issues:

1. (Quite major). It is impossible to switch the keyboard layout while in zathura: when I press Cmd+Space, the keyboard layout does not get changed, instead the page is scrolled. This is especially annoying, given that keyboard mappings do not work with non-latin keyboard layouts, so, if I happen to switch to a zathura window with a non-latin layout active, I have to switch back to another window and change the layout there.
2. (Minor). It would be better, in terms of UX, to replace Ctrl with Cmd in all shortcuts on macOS. I think this is what most cross-platform apps do.