On that note的英文定义: It typically is used to transition from one subject to another subject on the same topic. It's meaning can also be expanded to include associated emotions or feelings. This can be seen in similar expressions like: "On a happier note" or "On a sad note."
1. The speaker will say something amusing, profound or sombre and then say And on that note, ladies and gentlemen, I would like to end my address to you tonight.
People do use it when they mean in the context of that [just said], or leading on from that.
思考：感觉比 by the way 更正式点，如果你想在祝福邮件里说点别的事，用on that note 可能更委婉文雅些。