The staff ate it later

My inclination (as a non-native learner) would be to translate 美味しくいただきました as "the staff enjoyed it later". It's both slightly more formal and elegant-sounding than the comparatively coarse "ate", and captures the pleasure implied by 美味しく ("deliciously"). I would expect plain old "ate" if they used 食べました.

Of course, I'm not a professional translator or native speaker! It’s possible I'm over-indexing on the textbook knowledge I have of the language and in practice, to native Japanese eyes and ears, the things I think I'm seeing aren't really there.

In turn, I'm not a native English speaker, but in the dictionary I searched in, "enjoy" isn't a synonym of "eat", whereas いただく definitely is—albeit a very polite one[1].

[1]: https://jisho.org/word/%E9%A0%82%E3%81%8F