You can’t change the behavior
…
(Unless there’s a community plugin I don’t know about providing such feature
)
Date and Date & time keys needs to be written in Source mode following the ISO8601 format to be read/parsed/interpreted correctly by Properties in Live Preview which, in turn, displays that same ISO8601 formatted date (or date/time) according to your OS settings.
(And it goes both ways
: When you manually add a date or date/time value to a date or date & time key directly in Properties in Live Preview, it is also written in the YAML in Source following the ISO8601 format)
You can keep your current date format in the Templates core plugin and in the templates, when it comes to inserting a date or date/time value in Properties, you could use the placeholder {{date:YYYY-MM-DD}} instead of {{date}} to bypass the chosen date format set in the Templates core plugin so the value will be written as needed in Source and the date displayed in Properties should be the appropriate one.
Just in case: Here’s the related feature request
: