Are there locales or common programs that use YYYY-DD-MM as the date format?

See "Calendar date" on Wikipedia on the topic - it lists the countries by date/time format.

At first glance it doesn't look like anyone is using YYYY-DD-MM regularly.

yyyy-mm-dd in particular is a subset of the ISO-8601 format.

There is no recognised standard that uses year date month. When year is first, it should always be followed by an appropriate sub-year, be that quarter, month, julian day, etc.

Some advantages to using year-first is that the order also happens to work well for alpha-sorting when used as a text value (such as part of a file name).

You should try to get your team(s) to standardize on ISO 8601 formatting, or use it and tell everyone that's what you're using. Or see Wikipedia's ISO 8601 reference.