The reason I'm asking this is because I frequently need to refer to
*that version* of Python in the documentation, especially when I'm
deprecating APIs or behavior. Right now I'm saying "Python 4.0"
implying that 4.0 will be released right after 3.9.
I don't know what we'll end up calling it, but I don't think it matters for this. For warnings about future deprecations and removals, I would use "3.10" regardless.
No one can predict the future; maybe our future selves will change their minds when we get there. But for people reading the documentation now, "3.10" clearly means "the version after 3.9", so they'll understand what you mean. And if it ends up being called 4.0 then that's higher than 3.10 anyway, so no one can claim you didn't warn them.
OTOH if you write "4.0", at least some people will misunderstand, and be grumpy if the feature disappears in 3.10.