Thanks for uploading the sample project.
This issue should be fixed now in the latest sandbox build (2023.1.5487):
https://release.daypilot.org/changes/js/
Please let me know if it doesn't work as expected.
> On the other side, when I left click an existing time range selection, I expect the selection to be changed, which means, that the left clicked cell should be selected instead of the existing time range selection from before
Clicking an existing time range will not clear it - this is by design. There are onTimeRangeClick/ed, onTimeRangeRightClick/ed, and onTimeRangeDoubleClick/ed events that rely on this behavior.