A successful send makes a phone notification, which persists until removed
manually, but it is often unnecessary for me, as I mostly use Send file as a
quick alternative to bluetooth/cable to exchange files with the PC.

For example:
- if I have the PC in front of me, the PC notification is enough and
  auto-destroys after a few seconds;
- if the file is not to be used right away after receiving, e.g. I send
  and forget it, or send a big file and do another task.

What about an option to disable the notification or make it time-based?

For clarity, I do not ask for a general "don't disturb" mode (in fact I want
other notifications), but to disable it when already notified by other means.

I'm on kde connect 1.16 (not available as an option in bugzilla's form)