feat(docs): Check rustdoc more strictly (#1185)

This makes our docs checking a bit stricter:

    rustdoc warnings are now fatal in ci.
    we test docs of the entire workspace...
    we test private items as well

This includes the fixes needed to make this all work.

.github/workflows/ci.yml

@@ -9,6 +9,7 @@ on:
 env:
   RUST_BACKTRACE: 1
   RUSTFLAGS: -Dwarnings
+  RUSTDOCFLAGS: -Dwarnings
   MSRV: "1.65"
 
 jobs:
@@ -249,7 +250,7 @@ jobs:
       run: cargo fmt --all -- --check
 
     - name: Docs
-      run: cargo doc
+      run: cargo doc --workspace --all-features --no-deps --document-private-items
 
   clippy_check:
     runs-on: ubuntu-latest