Create `Atomic<T>` type alias (rebase)
Rebase of #130543.
Additional changes:
- Switch from `allow` to `expect` for `private_bounds` on `AtomicPrimitive`
- Unhide `AtomicPrimitive::AtomicInner` from docs, because rustdoc shows the definition `pub type Atomic<T> = <T as AtomicPrimitive>::AtomicInner;` and generated links for it.
- `NonZero` did not have this issue, because they kept the new alias private before the direction was changed.
- Use `Atomic<_>` in more places, including inside `Once`'s `Futex`. This is possible thanks to https://github.com/rust-lang/rust-clippy/pull/14125
The rest will either get moved back to #130543 or #130543 will be closed in favor of this instead.
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* ACP: https://github.com/rust-lang/libs-team/issues/443#event-14293381061
* Tracking issue: #130539
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