gh-37667: Fix noexcept clauses (#37560)
    
In #36507 I added a lot of `noexcept` clauses guided by a warning which
is not quite right (see
cython/cython#5999 (comment)).

A new warning in 3.0.9 shows the mistake (incorrectly added `noexcept`
clauses). This broke some doctests (#37560) and a workaround was
implemented for 10.3 (#37583) since we were too close to release.

This PR now does the proper fix, removing all the incorrect `noexcept`,
and also adding a few missing `noexcept`.

Note: if one tries this PR with cython <= 3.0.8 it seems it's wrong in
the sense that it will show 40k more warnings after the PR. These are
*incorrect* warnings.

If one uses cython 3.0.9 each of these 40k lines give a correct warning
before this PR and an incorrect warnings after the PR, and there is no
way to avoid 40k warnings.

To confirm this PR is a good one, one needs to use cython 3.0.9 +
cython/cython#6087 or wait for cython 3.0.10. In
this case, the warnings are correct and one will get 40k warnings before
the PR and no warning after the PR.

The last commit reverts the workaround from #37583 so we don't silence
these warnings on `cython()` now that we have our own code right.

@vbraun: this is "almost trivial" but touches too many files. Could we
merge it in beta0 to avoid conflicts? I did this "kind of" automatically
and I've been testing it for two weeks in almost all my builds. The
changes made should not affect behaviour at all in the legacy mode we
are using cython.

### 📝 Checklist

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URL: #37667
Reported by: Gonzalo Tornaría
Reviewer(s): Gonzalo Tornaría, Matthias Köppe

Author: Release Manager