The YYYY-MM-DD format is an international standard (ISO8601) which is used quite “broadly” across Obsidian (either natively or in some plugins).
In YAML (in Source Mode), this is actually how the values of date and date/time keys are stored and written on file while displaying, in Properties in Live Preview, these same values following, normally, a “Language & Region” setting at the OS level (There’s an open feature request regarding this: here 
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Now, I know some seem to have issues on Windows and Linux to have their date and date/time values displayed as they should 
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When it comes to the Tasks plugin, there seem to have been an opened (now closed) feature request for this