Fix rustdoc warnings and test cargo doc in CI (#4711)

## Problem

`cargo +nightly doc` is giving a lot of warnings: broken links, naked
URLs, etc.

## Summary of changes

* update the `proc-macro2` dependency so that it can compile on latest
Rust nightly, see https://github.com/dtolnay/proc-macro2/pull/391 and
https://github.com/dtolnay/proc-macro2/issues/398
* allow the `private_intra_doc_links` lint, as linking to something
that's private is always more useful than just mentioning it without a
link: if the link breaks in the future, at least there is a warning due
to that. Also, one might enable
[`--document-private-items`](https://doc.rust-lang.org/cargo/commands/cargo-doc.html#documentation-options)
in the future and make these links work in general.
* fix all the remaining warnings given by `cargo +nightly doc`
* make it possible to run `cargo doc` on stable Rust by updating
`opentelemetry` and associated crates to version 0.19, pulling in a fix
that previously broke `cargo doc` on stable:
https://github.com/open-telemetry/opentelemetry-rust/pull/904
* Add `cargo doc` to CI to ensure that it won't get broken in the
future.

Fixes #2557

## Future work
* Potentially, it might make sense, for development purposes, to publish
the generated rustdocs somewhere, like for example [how the rust
compiler does
it](https://doc.rust-lang.org/nightly/nightly-rustc/rustc_driver/index.html).
I will file an issue for discussion.

.github/workflows/build_and_test.yml

@@ -127,6 +127,11 @@ jobs:
       - name: Run cargo clippy (release)
         run: cargo hack --feature-powerset clippy --release $CLIPPY_COMMON_ARGS
 
+      - name: Check documentation generation
+        run: cargo doc --workspace --no-deps --document-private-items
+        env:
+            RUSTDOCFLAGS: "-Dwarnings -Arustdoc::private_intra_doc_links"
+
       # Use `${{ !cancelled() }}` to run quck tests after the longer clippy run
       - name: Check formatting
         if: ${{ !cancelled() }}