This seems like such an obvious answer to the problem, your program isn't truly modularized if logging is global. If an error is unexpected it should bubble all the way up, but if it's expected and dealt with, the error message should be suppressed or its type changed to a warning.
I’ve worked on systems with “modularized” logging. It’s never been pleasant because investigations involve stitching together a bunch of different log sources to understand erase actually happened. A global log dump with attribution (module/component/file/line) is far easier to work with.