Time off automation in Settings → Time tracking → Time Off

In https://use.operating.app/settings/time-tracking/time-off you can find a checkbox saying Automatically create time entries on public holidays.

If you enable this, it will start creating time entries (using the public holidays category) for each day early in the morning of that day. It will look at which Site the Person belongs to on that day. Thus, moving from one Site to another will work quite nicely.

If you check the checkbox, you will be presented with a button that adds missing public holiday time entries retroactively.

After you click Add missing public holiday time entries:

You can add time entries for public holidays that happened before your setup date. These time entries are created based on your holiday calendars. Choosing a date range will create time entries for any public holidays in that period.

Existing time entries for the "Public holidays" category won’t be duplicated. If a public holiday falls on a Saturday or Sunday, no time entry is created.