base/docs: Add missing compat notes and docs entries for 1.13 features (#61529)
Developed with Claude:
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Several functions and types introduced in Julia 1.13 were missing `!!!
compat "Julia 1.13"` annotations in their docstrings, and some were
absent from the API reference docs entirely.
Also ~declare `Base.setindex` as public in base/public.jl, which was
inadvertently omitted from the original PR (#59880)~, and fix `nth` →
`Iterators.nth` in HISTORY.md following the rename in #61486.
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Co-authored-by: Claude <claude@users.noreply.github.com>