In my last project team, we had a rule about follow-up emails... always add 'no rush' at the end. It changed how people responded, just like your client.
Adding "no rush" can actually backfire by making people feel watched. It plants the idea that speed is being measured, even if you say otherwise. The phrase often reads as passive pressure instead of real patience.
Seriously? We overthink this stuff way too much. Most clients just want clear timing and simple questions. If someone gets weird about "no rush", they were probably stressed already. Not every word needs a full team meeting to pick apart.