Minor fixes to core::io & alloc::io Documentation

[bushrat011899]

ACP: rust-lang/libs-team#755
Tracking issue: #154046
Supersedes: #160413

Description

Minor tweaks to the documentation in core::io and alloc::io after proof-reading. In #160413 I attempted to rewrite all example snippets to be no_std/no_alloc compatible where relevant. I've closed that in favour of smaller adjustments, as there are many examples of std-requiring code snippets in core documentation (e.g., core::borrow).

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Notes

• No AI tooling of any kind was used during the creation of this PR.

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[bushrat011899]

CI failure must be unrelated to this PR, unless there's some interaction between documentation and GCC I'm unaware of...

EDIT: See #160468

[rustbot]

This PR was rebased onto a different main commit. Here's a range-diff highlighting what actually changed.

Rebasing is a normal part of keeping PRs up to date, so no action is needed—this note is just to help reviewers.