Older versions of Nano didn't support Ctrl+arrow bindings out of the box, or not on all terminals. Recent versions should work, though. The version shipped with macOS is an antique 2.0.0 that doesn't support those keys and doesn't support configurable key bindings, so you're out of luck. But according to the package list, Ventura (13.0) stopped shipping Nano.
If you've installed Nano through Brew/Macports/Fink/…, make sure that you're invoking that one and not the one bundled with macOS. Run nano --version to check the version of the instance that you're calling. In zsh, run
type -a nano
to see where the nano executable(s) are. If this outputs multiple lines, the one that takes effect is the first line. If the output is something like
nano is /bin/nano nano is /opt/homebrew/bin/nano
then you need to arrange your command search path differently. Run
print -lr $path
to list your command search path. You can change it by modifying PATH or path in your ~/.zprofile.
If your Nano is recent enough (at least 2.1.0) but doesn't recognize Ctrl+arrow, you can set them up in your ~/.nanorc (that's the file called .nanorc, with a leading dot, in your home directory). Find out what escape sequences those key chords send in your terminal. (See https://unix.stackexchange.com/questions/47312/control-and-up-down-keys-in-terminal-for-use-by-emacs/47402#47402 and https://superuser.com/questions/357355/how-can-i-get-controlleft-arrow-to-go-back-one-word-in-iterm2 for similar answers and https://unix.stackexchange.com/questions/116629/how-do-keyboard-input-and-text-output-work/116630#116630 for a more thorough explanation of escape sequences.) At the zsh prompt, press Ctrl+V then Ctrl+Left then Ctrl+C. This inserts multiple characters, where the first character is the control character Escape, represented visually as ^[ (often in a different color). In your .nanorc, you'll need to use the two characters ^[. For example, if you see
^[[1;5D
(which is a common escape sequence for Ctrl+Left, and AFAIK is the one that both Terminal and iTerm2 send out of the box), you'll need to pass ^[[1;5D to the bind command in .nanorc. Repeat for Ctrl+Right and any other cursor key you want to bind. You can find command names in the nanorc manual (man nanorc on your system). Thus your nanorc should contain:
bind ^[[1;5D prevword bind ^[[1;5C nextword
opt+arrow keys, the default keybinding to do that in macOS. Setting modifier keys to work properly in iTerm or Terminal is confusing though, and I'm not sure what I should write in my .nanorc file.