I know a lot of chat tools use Enter to send the message and SHIFT+Enter for newlines. I have always found that infuriating as it is not how most text editors and even textareas on the web work, so I always end up submitting my message or prompt by accident.
I appreciate that the assistant wants to mimick a chat experience and therefore have the same defaults as chat apps. Yet, I also think that this default settings of chat apps is a bad one, particularly in apps that lend themselves to longer messages like I think is the case of the Kagi assistant.
Whatsapp, Slack, and others thankfully have a setting that allow Enter to be used for newlines and CTRL+Enter for submitting. I wish the Kagi assistant had that as well. In the meantime, a small note below the text input like "Use Shift+Enter to input a newline, Enter to submit" might help !
Have a setting that makes CTRL+Enter submit prompts and Enter create newlines.