This is a reasonable approach, but having a catch-all case that handles the exception and re-throws it, but wrapped in custom exception type can be problematic

This is a reasonable approach, but having a catch-all case that handles the exception and re-throws it, but wrapped in custom exception type can be problematic in case a new exception is added - the consumer of the API needs to go over their code and change the types everywhere, or else their catch code will not be working as before anymore. This problem can easily go unnoticed, judging by my Haskell experience. The solution would be to always use "checked exceptions" (or similar concept in your language, e.g. `ExceptT SomeEnumType` in Haskell) and never use catch-all cases (or wildcard patterns, in case of Haskell), so that every exception handling case is tagged with exception type, and type-checked.