macOS has 4 different date formats, Short, Medium, Long, Full. The date you are setting in your screenshot is Short and the date you're seeing elsewhere is Full. Up until Monterey, it was possible to control the display of each format individually. According to
this AppleSupport document, that is no longer the case in Ventura. If you select Monterey at the top you can read how to change them, but switching to Ventura, the extra options are gone. I would guess they're still available via shell commands, but I don't know what they are. There seems to be
support within Shortcuts for setting custom date formats, but I haven't used it.