This is an interesting perspective. I usually don't try to imagine how someone should handle the error. Instead I try to indicate the different types of errors that could occur and what type of information needs to be included to be useful to the caller. I can leave the question of what to do with that information to the caller since it's highly situational and the context necessary to make that decision lives outside of the code where I am modeling the error.
That can be tricky because there may be a trade-off between error message quality and something else. Like, perhaps, the size of an error, code size or even runtime performance. Another trade-off with too-detailed errors---especially when those details are part of the library API---is that they become an extensibility hazard. Unless you're extremely certain about the line that divides a specific implementation from the logical domain of errors for a particular operation, you might get that wrong. And changing the implementation in the future might want a change in the error details.
This is very hand-wavy, but I think we're talking at a very high level of abstraction here. My main point is to suggest that there is more of a balancing act here than perhaps your words suggest.