>"enjoy" isn't a synonym of "eat"

It isn't literally, but it takes on this meaning in context. If you "enjoy" ("receive pleasure or satisfaction from; have the use or benefit of" per M-W) food, it's hard to imagine that you did anything else with it (er, let's not explore that here, please).

It's much like how the primary, literal sense of いただく is more like "receive".

Itadaku is literally the kenjogo form of taberu (eat). It just happens to have multiple meanings.