Reduce warnings on CI from GitHub Actions (#5083)

* Upgrade our github actions to "node16"

Each github actions run has a lot of warnings about using node12 so this
upgrades our repository to using node16. I'm hoping no other changes are
needed and I suspect other actions we're using are on node12 and will
need further updates, but this should help pin down what's remaining.

* Update `actions/checkout` workflow to `v3`

* Update to `actions/cache@v3`

* Update to `actions/upload-artifact@v3`

* Drop usage of `actions-rs/toolchain`

* Update to `actions/setup-python@v4`

* Update mdbook version

.github/workflows/release-process.yml

@@ -38,7 +38,7 @@ jobs:
     name: Run the release process
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
         with:
           submodules: true
       - name: Setup