I’m not 100% sure about the error, but it looks like the nixos-unstable channel already has v0.25.2 for kitty. So you should be able to use that. There are instructions here for how to use select packages from unstable while using stable for the rest of your packages.
The error is because the base package expression tries to apply extra patches not compatible with 0.25.2 source code. You can see that the patches removed in the update commit:
Both of the above methods are working and the version 0.25.2 of kitty is installed in the nix store.
But wathewer method used, the symbolic link in ~/.nix-profile/bin/kitty is not updated and still point to the old version of kitty.
kitty --version
kitty 0.25.1 created by Kovid Goyal
/nix/store/wxhynx5if1g2q8pzdrkpm77hrnm9hq2k-kitty-0.25.2/bin/kitty --version
kitty 0.25.2 created by Kovid Goyal
nixos-rebuild does not take care of your profile (unless you use something like home-manager through NixOS). Most likely ~/.nix-profile/bin/kitty was installed by nix-env.
Check nix-env -q for packages installed by it and nix-env -e kitty to uninstall. Then kitty from system-wide profile should be picked up.