If you’re lucky, you’ll even get a PR 
I think adding it is enough, and release as you would following your normal schedule. It’s a useful signal to your users that you have tested and believe you have support. We can check the repo if there’s no classifier on PyPI yet. (Tip: add it already during your pre-release testing.)
Good news on all fronts!
There’s a new RSS feed you can follow that will notify for each release, including RCs: Python Releases
I’ve hooked it up to this Mastodon bot: Feed for python_releases
3.13 has been available on actions/setup-python since alpha 1: Add Python 3.13.0 alpha 1 · Issue #742 · actions/setup-python · GitHub
And for cibuildwheel since beta 1: Release v2.18.0 · pypa/cibuildwheel · GitHub
Cython is more challenging, as it’s more sensitive to C API changes, but they’ve also had preliminary support for 3.13 since alpha 1 to allow early testing: Cython Changelog — Cython 3.1.0a0 documentation
In fact, we also reverted some C API changes at the start of the alpha for the benefit of early testing with Cython: Python 3.13 alpha 1 contains breaking changes, what's the plan?
Meaning it’s been possible for many to test for a year before the big final release, and to create wheels to help others test for 6 months. I think the main blocker has generally been a lack of pre-release wheels from dependencies.