Switch to rust-toolchain@master in "Update GitHub Pages" (#2613)

## Motivation and Context
The previous attempt #2610 did
not work for properly running the workflow for `Update GitHub Pages`.
This PR reverts it and uses a different fix to address the issue.

## Description
Possibly with
[this](https://users.rust-lang.org/t/sparse-registry-breaking-my-ci-and-i-dont-understand-why/89976)
and `dtolnaly/rust-toolchain` having fixed a couple of issues [related
to the sparse
registry](https://github.com/dtolnay/rust-toolchain/issues?q=is%3Aissue+is%3Aclosed+sparse)
recently, this PR will use `dtolnaly/rust-toolchain@master` rather than
`stable` (most CIs in this repository have been using `master`).

## Testing
The workflow in question has been verified to run successfully with this
change
([link](https://github.com/awslabs/smithy-rs/actions/runs/4758820036)).

----

_By submitting this pull request, I confirm that you can use, modify,
copy, and redistribute this contribution, under the terms of your
choice._

---------

Co-authored-by: Yuki Saito <[email protected]>
Co-authored-by: John DiSanti <[email protected]>

.github/workflows/github-pages.yml

@@ -1,18 +1,15 @@
 on:
   workflow_dispatch:
-    inputs:
-      opt-in-to-sparse-registry:
-        description: Enable/disable CARGO_UNSTABLE_SPARSE_REGISTRY (https://blog.rust-lang.org/2022/06/22/sparse-registry-testing.html)
-        required: true
-        type: boolean
-        default: false
   push:
     branches: [main]
     paths:
     - design/**
 
 name: Update GitHub Pages
 
+env:
+  rust_version: 1.67.1
+
 # Allow only one doc pages build to run at a time for the entire smithy-rs repo
 concurrency:
   group: github-pages-yml
@@ -26,11 +23,12 @@ jobs:
       uses: actions/checkout@v3
       with:
         persist-credentials: false
-    - uses: dtolnay/rust-toolchain@stable
+    - uses: dtolnay/rust-toolchain@master
+      with:
+        toolchain: ${{ env.rust_version }}
     - name: Generate docs
       env:
         GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-        CARGO_UNSTABLE_SPARSE_REGISTRY: ${{ inputs.opt-in-to-sparse-registry }}
       run: |
         git config --local user.name "AWS SDK Rust Bot"
         git config --local user.email "[email protected]"