GitPython is compatible with Python 3.13 on Unix-like systems, and it is believed to be mostly compatible with Python 3.13 on Windows, but there is an incompatibility due to a Windows-specific breaking change in Python 3.13 related to how one of the standard library functions classifies paths as relative or absolute.
In practice, I think it is highly likely to work already for most users on Windows, but we do have a failing test on 3.13 on Windows, and there may be realistic scenarios where users on Windows would encounter problems with GitPython on Python 3.13--either in connection with the code exercised by that test, or in connection with other code that no test currently exercises in a way that relates to the incompatibility. (Regarding CI, we run CI on Python 3.13, but not with that version on Windows currently.)
See #1955 for full details. I hope to get to this sometime soon, especially with Python 3.14 being just around the corner, but unfortunately I do not know when I'll get to it. Alternatively, if someone else wants to complete that, it would definitely be fine with me. I think that, at a minimum, the three "Windows:" steps related to absolute paths should be done before adding the classifier that explicitly declares Python 3.13 compatibility.
I can imagine an argument for considering Windows to be a secondary platform, such that it would not have to wait on this. But I think many users of software that depends on GitPython are likely running Windows, so that would probably not be a good idea. @Byron please let me know if you have a position on this.
Regarding the metadata, please note that while we do currently list trove classifiers indicating compatibility with some versions of Python that are well tested and specifically believed to be compatible, the actual hard specification states no upper bound and permits installation on Python 3.13 on all systems:
However, I understand that's not a declaration that, in practice, there is no degradation on 3.13. Accordingly, I understand that this, by itself, is probably not what you're looking for.