Unfortunately, kitty's author has a strong dislike for terminal multiplexers, and it shows in his designs. Recent updates to kitty have broken out-of-the-box functioning of terminal multiplexers. It may be possible to get them working with some configuration tweaks. But Kitty's configuration is huge - I don't have the energy to figure it out. So, I had to abandon kitty in favor of foot terminal emulator.
The author may be justified in his dislike for terminal multiplexers. They were created at a time when emulators were too dumb and didn't have enough capabilities. Multiplexers break some functionalities on modern emulators. But I wish software authors in general respected that there is no one-size-fits-all solution and made their design to be more general purpose. In this specific case, I wish there was some standard protocol for terminal emulators and multiplexers to cooperate.
The author is well within his right to choose his designs and I unfortunately don't have the time to solve that problem. And that leaves me giving up kitty as the only solution. But I miss some innovations that kitty brought to the table - new graphics protocol, remote control protocol etc. I hope that those protocols will be widely implemented in other emulators too.