If I, as a regular Google user ask in the search "is this search powered by Gemini?", the AI generated result is in the affirmative.

"Yes, this search is powered by a customized version of the Gemini model for its generative AI features."

Based on that, I'm not sure how it is reasonable to claim that Gemini App has a legal term that is exclusive of its use in search.

Amusingly, it refuses to answer if i ask "is this search powered by Gemini app?"

What? The paper clearly says "This section presents the environmental impact metrics for the Gemini Apps AI assistant". You are going through lots of hoops instead of just reading the paper.