Personally if I wanted to make breaking changes to a released, v1.x.y package, I’d release it as v2.0.0 with a new import path, so as not to break any existing users (whether or not they use a package manager, and most do not!). Then if I were to break it again, I’d issue another major release.
If I could, I’d try to make both breaking changes at the same time, to avoid making my users migrate twice. (And also to avoid having to continue to support the in-between major version.)
In the long run you’ll end up with a much less confusing situation if you give new major versions new import paths, particularly if you intend to continue supporting the v1 series. Looking at a piece of code, you’ll be able to see immediately which version of the library is in use, regardless of the package manager setup (or absence thereof). That’ll be a huge benefit in supporting your users.