CI is very red, but all of the failures look very unrelated (internet or file system) and master has been red for a while.

Oops. Only now did I realize that a docstring update may still be needed. I expect there are situations where an InexactError may still be thrown (or could be for some other types), so that part should still be there, but the current docstrings don't address the new behavior introduced in this PR.

I expect there are situations where an InexactError may still be thrown

I don't think so

julia> Base.infer_effects(round, Tuple{Type{Float64}, Int})
(+c,+e,+n,+t,+s,+m,+u)

or could be for some other types

Yes:

julia> floor(UInt8, 1000)
ERROR: InexactError: trunc(UInt8, 1000)

We also have

floor(T, x) converts the result to type T, throwing an InexactError if the floored value is not representable a T.

in the docstring already.

the current docstrings don't address the new behavior introduced in this PR.

Do you have a specific behavior that isn't documented? For the most part I think this PR is doing a bugfix to change behavior to match what was already quasi-documented.

Sorry. You're right. It's all covered. I just looked at this first thing in the morning and my brain wasn't working. It talks about rounding to representable values.