> Those 10 days certainly exist, in both calendar systems.

Not in the standard Gregorian calendar. Those dates only exist in the proleptic Gregorian calendar. The standard Gregorian calendar explicitly skips them. That's because you can't feasibly go back and change all the Julian dates that had been physically written down for centuries. That's why it's called the Gregorian "shift".

Messiness is an understatement :)

Thanks. I haven’t known that countries switched in different years.

Gregorian calendar is just one piece.

https://en.wikipedia.org/wiki/Civil_calendar

Eighteen countries use another calendar alongside the Gregorian calendar…