I ran some experiments on my fork to test pyerfa against CPython 3.13. I report that current wheels are already compatible with the GIL-enabled build for 3.13.0b2 (which is expected with abi3 wheels, restricted to Python's limited API).
update: #153

However, the free-threaded build isn't compatible yet. Attempting to build pyerfa will explicitly fail with the following error

In file included from erfa/ufunc.c:14:
        /opt/_internal/cpython-3.13.0b1-nogil/include/python3.13t/Python.h:51:4: error: #error "The limited API is not currently supported in the free-threaded build"

Here's the upstream issue to wait on before we can move forward python/cpython#111506