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

## Motivation and Context
The previous attempt https://github.com/awslabs/smithy-rs/pull/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)

).

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choice._

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Co-authored-by: Yuki Saito <awsaito@amazon.com>
Co-authored-by: John DiSanti <jdisanti@amazon.com>