I realize it's probably a toy example but specifically for "cats" you could achieve the similar results by running a thesaurus/synonym-set on your stem words. With the added benefit that a client could add custom synonyms, for more domain-specific stuff that the LLM would probably not know, and not reliably learn through in-prompt or with fine-tuning. (Although i'd argue that if i'm looking for cats, I don't want to also see videos of tigers, or based on the "understanding" of the LLM of what a cat might be)

For the labeling of videos itself, the most valuable labels would be added by humans, and/or full-text search on the transcript of the video if applicable, speech-to-text being more in the realm of traditional ML than in the realm of GenAI.

As a minor quibble your use case of GenAI is not really "Generative" which is the main thing it's being sold as.