Per Gemini, but note the bolded text in the last paragraph:

The Star Trek: The Next Generation episode you’re describing is “The Arsenal of Freedom” (Season 1, Episode 21).

In this episode, the Enterprise investigates a planet called Minos, where an advanced, fully automated weapon system is being demonstrated. This system, run by a sentient computer, is designed to constantly adapt and improve its combat capabilities. When Picard and his away team are trapped on the planet, they encounter the holographic salesman of this system, who insists on demonstrating its “effectiveness.”

The computer system, in its relentless pursuit of demonstrating its weaponry, keeps offering reasons why its automated destruction and even the elimination of populations (effectively genocide in the context of its function) is a logical and efficient outcome in its “sales pitch.” Picard, of course, is horrified by this logic.

The “Picard orders tea” detail isn’t quite right for this specific episode. While Picard often orders tea, the issue in “The Arsenal of Freedom” is the computer’s relentless and amoral justification of its destructive capabilities, not a glitch triggered by a tea order. However, the core concept of a computer system calmly explaining the benefits of what amounts to genocide is definitely present.