As a KDE Connect user for a few years I know it doesn't always work without reconnecting especially with sleep cycles on the phone and the laptop but it does everything on Android at least - clipboard sync, notifications, sms, calls, remote control and media playback control. Must be iOS restrictions that made the author go through the admirable effort.
IOW Linux ecosystem has better vertical integration without any direct ties with Android :)
Does KDE connect work with other, non KDE window managers?
Yes, and it's great. But you can't iMessage / SMS or get Notifications with iPhone.
My absolute favorite feature in KDE Connection is full audio device output / input control remotely so I can silence notifications without getting up or start playing music through the speakers.
It even works on Windows.
yes, there's even a GNOME shell extension[0] that implements the KDE Connect protocol without needing the official KDE version.
[0]: https://github.com/GSConnect/gnome-shell-extension-gsconnect