#[0] I was just testing out sending private messages over a relay and I have some info:
If my mutual relay with the private message receiver is temporarily offline while I am typing messages to them, they will not receive any of the messages that I sent and the relay does not seem to notice and send the messages once back online. The result is the receiver of my messages doesn't receive the message and I am unaware as the sender that they did not receive the message.
I'd suggest something to make it clear that the private message you sent has not been broadcast over any mutually shared relays and perhaps an option to 're-send' messages that are flagged as 'not been broadcast'.
I hope that makes sense, happy to clarify but thought this may be useful for you to know.