fix(ci): pin the nightly that renders the public-api baselines

[h4x0r]

What was wrong

The workflow pins cargo-public-api to 0.52.0, with a comment saying that keeps
its "textual output format stable across CI runs". On its own it does not.
cargo-public-api renders from rustdoc JSON, so the nightly that produces
that JSON decides the output text as much as the tool version does — and the
nightly was installed unpinned:

run: rustup toolchain install nightly --profile minimal

A recent nightly moved io into core, so the renderer began emitting
core::io::error::Error where the committed baseline says
std::io::error::Error. The gate reported a public API change on an API that
had not changed at all:

-pub fn ... -> std::io::error::Result<...>
+pub fn ... -> core::io::error::Result<...>

The fix

Pin the nightly, so both inputs to the rendering are fixed.

Verified rather than assumed: rustc +nightly-2026-05-12 --version reports
1.97.0-nightly (64a965e90 2026-05-11), and regenerating every baseline in this
repo with that toolchain diffs against the committed files by zero lines.

Note the off-by-one — rustc reports its commit date, one day behind the
toolchain name — so nightly-2026-05-11 would have been the wrong pin. That is
why the date was checked by installing it, not inferred from rustc --version.

No baseline changes are needed, because the pin selects the toolchain the
baselines were generated with. Bumping NIGHTLY from here is a deliberate act
that regenerates the baselines in the same commit; moving one without the other
is exactly what produced this failure.

Fleet context

All 10 repos with a public-api workflow floated nightly, and all 10 get the
same pin. Three had already fired. The other seven are green only because their
public APIs contain no io types — nothing to re-render — not because their
pinning worked; they were equally exposed to the next rustdoc change.