Tried the following example to show context menu with library version DayPilot Pro for JavaScript 2021.2.4931 but seems does not working. No matter I right clicking on event or time range the context menu shows "Show range". It this function was obsoleted or it is a bug?
It should work fine for both the time range selection (use right mouse button to make the selection) and events.
The latest version seems to have a bug that doesn't allow you to invoke the context menu on the existing time range selection. That is fixed in the latest sandbox build (2021.3.5045):