I wonder if something similar goes on in Klingon, not with animals,
but with computers that have a natural language interface. Would a
Klingon who used such a computer regularly start to unconsciously
refer to the computer as a ghaH?
This doesn't directly answer your question, but in English, ships are "she", while in Klingon, they're {'oH}. While Federation ships talk (or their computers do), the only instance I can recall of a Klingon talking ship or computer is in Discovery. (There's a scene where a device announces something about atmospheric pressurisation to L'Rell, but it's very brief and she does not refer to the device by a pronoun. But in any case, the Klingon wasn't written by Okrand.)