How to update event text value after click on a button.

You need to get the DayPilot.Event instance first using events.find(). Then you can update the event using events.update().

const dp = this.scheduler.control;
const e = dp.events.find("1");
e.data.text = "new text";
dp.events.update(e);

See also:
https://api.daypilot.org/daypilot-scheduler-events-find/
https://api.daypilot.org/daypilot-scheduler-events-update/

If you use the [events] attribute you can simply change the event properties in the source array and the Scheduler will be updated automatically. But you should know that using the [events] affects performance:
https://doc.daypilot.org/scheduler/angular-performance/