I do a bit of spreadsheet work and in the course of that run across differing date formats. All of the spreadsheet types I use (Excel, Gnumeric, and LibreOffice Calc) are pretty adept at converting the existing format to one which may be more acceptable in various applications. Any of the statistical packages such as SAS, SPSS, etc handle a variety of date/time formats.Even if the date is formatted as text rather than as a date, it can be handled.
In some posts I did several years years ago, this issue was brought to my attention as I was using the mm/dd/yy format. I changed to the alpha for for the month and went with the 4 digit year. This eliminated any confusion as to what date was referenced i.e January 01, 2021.
As to how the dates appear on the website, that is up to the web designers. I can get used to just about any format as long as I know which one is being used.
Cheers

Yes, context is the key. Interesting, I did not know there is a format which used a 3 digit year. I am also thankful they are not using a Julian date format.
Cheers

YYYY-MM-DD is big-endian and is perfect.
DD-MM-YYYY is little endian for the date portion, but then the time that follows is always big-endian (HH:mm:SS).
MM-DD-YYYY is some kind of weird middle-endian monster. It hurts my brain. :-)

Maybe because there's a simple answer: mm/dd/yyyy is idiotic, where dd/mm/yyyy isn't ;
dd/mm/yyyy (or dd-mm-yyyy or dd.mm.yyyy or dd mm yyyy) is more logical.

Nearly every country in the world uses some form of DMY or YMD, except American Samoa, Federated States of Micronesia, Guam, Marshall Islands, Northern Mariana Islands, United States Minor Outlying Islands, United States Virgin Islands.
Nearly all countries don't use MDY (Australia uses MDY sometimes, Eritrea sometimes, Guinea sometimes, Hong Kong rarely, India sometimes, Nepal sometimes, Norway rarely, Palau rarely, Singapore sometimes, Sri Lanka rarely, United Kingdom rarely, Vietnam sometimes).
(See Wikipedia.)