For a software, I have two different branches, that only differ in using different library versions of a package, that my software uses. The API of this library has changed between the versions in a non-compatible way.

I am currently developping using the new version, but the older version is still around on various systems.

Should I release these packages with different version names using Semantic Versioning? In my opinion, yes, but what about the naming of these different versions?

Currently I am using the "normal" numbering using the new version of the third-party library, e.g. 1.0.0, and a suffix for the version using the older third-party library, e.g. 1.0.0+json-c-0.10.

I will backport all changes to the code using the new version of the library to the other version, at least as long as the old version of the library is still around, so featurewise all releases of my software come with the same set of functions, but different dependencies.