How to change opacity of the backcolor of the event?

You can add a custom CSS class to the event using cssClass property of the data object:

// e is the DayPilot.Event object
// dp is the DayPilot.Scheduler object
e.data.cssClass = "semi-transparent";
dp.events.update(e);

See also:
https://api.daypilot.org/daypilot-event-data/

I tried that with no effect, then my colleague used e.client.cssClass and dp.events.update(e).notify() which worked. Also, he created new class - do I understand correctly that it was not a name of the actual class, but just a suggestion?

It's not necessary to call notify() but it is necessary to define the CSS class. That was just an example that shows how to assign a custom class to the event. The scheduler only defines classes that are part of the default theme (starting with "scheduler_default").

An example definition would look like this:

.semi-transparent {
  opacity: 0.4;
}

Thanks, Dan. It all works nicely now. I misunderstood your original suggestion and thought the Pilot already had its own css file. I then searched our project and found this not to be the case (but my colleague already created new css with several custom classes).

The other difference is that he used e.client instead of e.data.