[ci] Update 'Build docs' job to use nightly-2021-03-23

[notmandatory]

Description

This change is required because latest nightly (2021-04-11) rustdoc is showing what appear to be invalid errors like:

error[E0642]: patterns aren't allowed in methods without bodies
Error:     --> /home/runner/.cargo/registry/src/github.com-1ecc6299db9ec823/clang-sys-0.29.3/src/lib.rs:2186:46
     |
2186 |     pub fn clang_VerbatimLineComment_getText(comment: CXComment) -> CXString;
     |                                              ^^^^^^^
     |
help: give this argument a name or use an underscore to ignore it
     |
2186 |     pub fn clang_VerbatimLineComment_getText(_: CXComment) -> CXString;
     |  

Notes to the reviewers

There may also be a way to exclude building docs for clang-sys but I'd rather setup our CI to depend on fixed tool chain versions anyway so that we don't get random failures like this.

I also replaced actions-rs/toolchain and actions-rs/cargo with the equivalent run: commands, which is what we are already doing in our build-test CI jobs.

Checklists

All Submissions:

• I've signed all my commits
• I followed the contribution guidelines
• I ran cargo fmt and cargo clippy before committing