In the ISO week date system[1], 2021-01-03 is in the year 2020. Under the system all weeks have 7 days and start on Monday. The tradeoff is that the ISO year is out of sync with the calendar year around the end/beginning of the year.

[1] https://en.wikipedia.org/wiki/ISO_week_date

Strictly speaking, that's the case all over the world.

The beginning of the year used to be the Spring Equinox, which was March 1st. Somewhere along the line we jumped forward two months and the year started on January 1st, therefore making misnomers of the 7th (septem-ber), 8th (octo-ber), 9th (novem-ber), and 10th month (decem-ber) of the year. January should be the 11th month, and February should be the 12th month, which is why the leap day is on February 29th or the 'last' day of the leap year.

Even the date of the Spring Equinox got out of whack, March 21st instead of March 1st, when the Julian Calendar was changed to the Gregorian Calendar, and we jumped forward by enough days to 'fix' the Calendar. In reality, we should have just added sufficient 'leap days' to keep the Spring Equinox in its rightful place.