To format a date field into a calculated field in this way, you would have to build this yourself, "from scratch".
I recommend you start this by going through the calculated data expressions page.
https://experienceleague.adobe.com/en/docs/workfront/using/reporting/reports/calculated-custom-data/calculated-data-expressions
In particular, look up functions like "year", "month" and "dayofmonth". For the final restriction, look at the "case" function. Feel free to share your work back to this group as I know folks are always interested in looking at each other's solution.
edited to add: I ran this through copilot, and it suggests "if the length of your month or day = 1, add a zero" as an alternative to "case", so -- your call.