There is no option to click on the header and sort a column in the Modern UX's Tasks Timeline view. What column is this view sorted by?
A sample screenshot is shown below.
The Tasks Timeline view is sorted by "WBS Sort" column. This column can not be displayed in the Timeline View. It can however be displayed in the Grid View. The values of this column are set by ordering/reordering Tasks through PPM Gantt.
Therefore, the Tasks Timeline view shows the exact order in which Tasks appear in PPM Gantt. Changing the order in PPM Gantt will result in order of Tasks changing in Tasks Timeline view as well.
Status Report also sorts Task names by "WBS Sort" column.