well, for sure there are many axis to over engineering. I would say that a system that exceeds some specification is "over engineered" while on that is below the spec is "under engineered". At least I think that's the common use of the term.
I guess "expensive" might fall under costs, so something that was targeting a cost of $1000 but the design costs a million dollars to make is certainly over engineered.
I'd consider load ratings of an elevator to be similar. We mandate those are over-engineered by some margin. But if the load rating of an elevator is 1 ton and you designed an elevator to be able to carry 100 ton then it's certainly over-engineered by more than the safety requirements...
There are plenty of cases where exceeding the requirement is cheaper / easier / simpler than to try to match it more closely because you have some common and standard, hence cheaper, parts available.
So IMHO over and under engineering doesn't refer to the requirements, but to the engineering effort deployed.
I agree the terminology is sometimes used in this sense. Though if there is a bigger engineering effort it's often because the engineers are attempting to go beyond the requirements. I.e. the requirements may be satisfied with SQLlite on a raspberry Pi but the engineer builds a large distributed system that runs in the Cloud. This could just be because they have no idea what they're doing, or it could be because they're intentionally building something beyond what is asked. It's definitely possible to build more complicated systems that just barely satisfy the same requirement that a simpler system would satisfy. I'm tempted to call this "bad engineering" rather than "over engineering".
I guess "expensive" might fall under costs, so something that was targeting a cost of $1000 but the design costs a million dollars to make is certainly over engineered.
I'd consider load ratings of an elevator to be similar. We mandate those are over-engineered by some margin. But if the load rating of an elevator is 1 ton and you designed an elevator to be able to carry 100 ton then it's certainly over-engineered by more than the safety requirements...