chore(ci): Cleanup previous workflows after documentation versioning (#1973)

## Description

This PR deletes an older Github Actions Workflow which deploys the
in-development docs to the `gh-pages` branch. This workflow is not
needed going forward as we have switched to versioned documentation in
the `versioned-gh-pages` branch

## PR Checklist

> Thank you for opening a Pull Request! Before submitting your PR, there
are a
> few things you can do to make sure it goes smoothly:

- [x] Make sure you reviewed

[CONTRIBUTING.md](https://github.com/googleapis/genai-toolbox/blob/main/CONTRIBUTING.md)
- [ ] Make sure to open an issue as a

[bug/issue](https://github.com/googleapis/genai-toolbox/issues/new/choose)
  before writing your code! That way we can discuss the change, evaluate
  designs, and agree on the general idea
- [x] Ensure the tests and linter pass
- [x] Code coverage does not decrease (if any source code was changed)
- [x] Appropriate docs were updated (if necessary)
- [x] Make sure to add `!` if this involve a breaking change

🛠️ Fixes #<issue_number_goes_here>

.github/workflows/docs_deploy.yaml

@@ -1,79 +0,0 @@
-# Copyright 2025 Google LLC
-#
-# Licensed under the Apache License, Version 2.0 (the "License");
-# you may not use this file except in compliance with the License.
-# You may obtain a copy of the License at
-#
-#      http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software
-# distributed under the License is distributed on an "AS IS" BASIS,
-# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-# See the License for the specific language governing permissions and
-# limitations under the License.
-
-name: "docs"
-
-permissions:
-  contents: write
-
-on:
-  push:
-    branches:
-      - main
-    paths:
-      - 'docs/**'
-      - 'github/workflows/docs**'
-      - '.hugo/**'
-
-  # Allow triggering manually.
-  workflow_dispatch:
-
-jobs:
-  deploy:
-    runs-on: ubuntu-24.04
-    defaults:
-      run:
-        working-directory: .hugo
-    concurrency:
-      group: ${{ github.workflow }}-${{ github.ref }}
-      cancel-in-progress: true
-    steps:
-      - uses: actions/checkout@93cb6efe18208431cddfb8368fd83d5badbf9bfd # v5
-        with:
-          fetch-depth: 0 # Fetch all history for .GitInfo and .Lastmod
-
-      - name: Setup Hugo
-        uses: peaceiris/actions-hugo@75d2e84710de30f6ff7268e08f310b60ef14033f # v3
-        with:
-          hugo-version: "0.145.0"
-          extended: true
-
-      - name: Setup Node
-        uses: actions/setup-node@2028fbc5c25fe9cf00d9f06a71cc4710d4507903 # v6
-        with:
-          node-version: "22"
-
-      - name: Cache dependencies
-        uses: actions/cache@0057852bfaa89a56745cba8c7296529d2fc39830 # v4
-        with:
-          path: ~/.npm
-          key: ${{ runner.os }}-node-${{ hashFiles('**/package-lock.json') }}
-          restore-keys: |
-            ${{ runner.os }}-node-
-
-      - run: npm ci
-      - run: hugo --minify
-        env:
-          HUGO_BASEURL: https://${{ github.repository_owner }}.github.io/${{ github.event.repository.name }}/
-          HUGO_RELATIVEURLS: false
-
-      - name: Deploy
-        uses: peaceiris/actions-gh-pages@4f9cc6602d3f66b9c108549d475ec49e8ef4d45e # v4
-        with:
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_dir: .hugo/public
-          # Do not delete previews on each production deploy.
-          # CSS or JS changes will require manual clean-up.
-          keep_files: true
-          commit_message: "deploy: ${{ github.event.head_commit.message }}"