Lots of the commands have AddCommand inverted and I'm getting no completions out of it.

-	lsCmd.AddCommand(atCmd)
+	atCmd.AddCommand(lsCmd)

Commands without a Run function are ignored by cobra which is why there was no completion of the subcommands.
You can build and test it like this: https://carapace-sh.github.io/carapace-bin/development/build.html#development

Comparing the completions with the bridged (native) ones is also possible:

carapace --diff kitten/kitten kitten ...

They don't necesarily need to be the same though. Native completions often lack specific flags or there are opiniated differences.