In my configuration, f1 is bound to something at the i3-level.
When in kitty I type ctrl+shift+u, and get to the unicode input kitten, then switch to f2 for names, I can't go back to f1, because it's captured by i3.
If restarting the kitten made it go back to f1 mode, it would be good enough of a workaround, but it doesn't, and it probably shouldn't.
Can there be a ctrl+tab/ctrl+shift+tab in unicode input mode that switches to the next/prev search mode?