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It is good, that KDE alarms widget preserve alarms between sessions. Maybe made it working also, when computer is turned off? People always had smartphones turned on, so why not allow to send alarm/timers to cell phone and vice-versa?

That would be a job for KDEConnect. It should be possible to implement an extension to synchronize the data. But much more tricky to make the timers share their data, since there is no standard API or ABI for such task. Maybe some timer exposes some feature on DBUS, but this is completely up to the timer implementation.