Instead of using the Scheduler time header to display the navigation, it's better to create your own toolbar and place it above the Scheduler.
To learn how to implement the next/previous/today buttons, please see the documentation:
https://doc.daypilot.org/scheduler/next-and-previous-buttons/
You can highlight the time header using onBeforeTimeHeaderRender event handler. In this tutorial, you will find an example that highlights holidays:
https://code.daypilot.org/93068/javascript-scheduler-displaying-holidays
You can use the same mechanism to highlight the current day.
Another option is to use the built-in CSS. The current time header cell is marked with "scheduler_default_timeheader_cell_now". It is sliding automatically - it's not necessary to update the Scheduler periodically.
By default, there are no styles defined for this class. To highlight the cell, you'll need to add custom CSS definition.