How to stop Gemini being offensively obsequious?

Welcome to the forum.

That sentiment might be too harsh, but the main point of your argument is valid. Compare the responses from Gemini to those you get from Mistral; Mistral wastes no tokens apologizing, it accepts the correction provided by the user in a follow up prompt and immediately goes back to work solving the pending task. It’s the European thing to do. Claude Sonnet and GPT also engage in sycophantic behavior (“What a smart question!” or similar) and do unnecessary apologies, to a lesser degree than Gemini. Presumably the US based LLM providers use the same consultants that have told them that using modest psychological manipulation to make users feel good is good for the bottom line (and they probably don’t mind the extra revenue from token generation, a large number of small amounts adds up).