This appears to be a recent bug, maybe introduced in the last few weeks.
Prior to this, Assistant would always respond in the language of the prompt. This is useful because it doesn't make sense for a bilingual person to have to go update Kagi language preferences every time they want to change Kagi Assistant's output language.
Recently, Assistant is strongly preferring the language set in Kagi UI settings.
When prompted in English, Kagi Assistant (Quick model) will either immediately, or after several exchanges, switch to the UI language.
Instructing the model to switch to English is not effective. It either doesn't work, or Assistant reverts back to the UI language after several more exchanges.
For the reason above, I believe this instruction needs to be hard wired at deeper level than the user prompt, as it appears to be getting overruled.
I can't speak for everyone's preference, so perhaps there should be a setting for the preferred Assistant language, with an option to use the model's best judgement based on the incoming prompt.