Update ARMI docs to Python 3.13

[john-science]

ARMI wants to leave as many of its dependencies unpinned as possible for run time code. It's important that we can support as wide a variety of downstream user environments as possible.

But we pin our documentation dependencies, so we can get the exact look-and-feel we want in our docs, without them changing in us in a surprise. That's fine.

But ARMI's doc dependencies are getting old. They are based on Python 3.9, for one.

I would like it if we could update all our doc dependencies to (roughly) the latest versions of everything.

But the big lift here is testing to make sure all the features of the ARMI docs still work and look good.