Let's say that the creator of the interface allows IOException, but the backend of my implementation is a database so I have SQLExceptions, same issue.
Is the creator of the interface supposed to add every checked exception in the standard library? Ignoring that this still isn't all of them, then the caller is hosed because they have to handle (or rethrow) every single one of them which is no better. So they probably go "fuck it" and just handle / rethrow Exception. At which point you can just do that on the interface, and it's not helping anyone, and you're better off just not saying anything.
Checked exceptions simply don't mesh with the language: because the language provides limited to no way to abstract over them they're an issue every time you're trying to be generic over anything, the only situation in which they kinda sorta work is if the entire callchain is concrete, which not only is very limiting but it's very much not idiomatic.