Hi Marilyn,
Good question!
La Sainte Catherine is a festival for 'unmarried women'.
Probably not allowed to say this now and a bit irrelevant when people nowadays don't get married to form a family but in my youth, 'coiffer Sainte Catherine' meant you were on the shelf!
I know about hats being worn by any unmarried woman aged at least 25 but don't know anything about eating cake.
Please take a look at this wiki page which is quite informative.
https://fr.wikipedia.org/wiki/F%C3%AAte_de_la_Sainte-Catherine
Hope I haven't offended anyone, if so it wasn't my intention.