I saw tank tops, shorts and flip flops/sandals everywhere except for the indoor restaurant that offers the Columbian themed food. I would recommend nicer clothes for that one.
Bathing suits with covers and sandals are accepted for the 24-hour restaurant open to all. However I believe proper shoes and beach wear with or without cover-ups are not permitted in all the specialty restaurants (i.e. Steakhouse etc.)
Get an answer from Occidental Cartagena staff and past guests.