I like that, and if day of week is relevant:

    20230915sepFRI

Or for a legibility/size tradeoff:

    2023.09.15.sep.fri

All that left is adding the Chinese zodiac year!

    2023.09.05.rab.sep.fri

Now I am just slightly bothered that the abbreviated words don’t form an isomorphic representation to the numeric. :(

    2023.09.05.3watrab.sep.3fri

3rd Friday in September, 3rd Water Hare starting 1903! :)