Chore: Actions updates and cleanup (#8377)

## Summary

...

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-8377-WIP-Chore-Actions-updates-and-cleanup-2f66d73d3650818483a8dffa32a6f245)
by [Unito](https://www.unito.io)

---------

Co-authored-by: Amp <amp@ampcode.com>

.github/actions/setup-playwright/action.yml

@@ -1,28 +0,0 @@
-name: Setup Playwright
-description: Cache and install Playwright browsers with dependencies
-runs:
-  using: composite
-  steps:
-    - name: Detect Playwright version
-      id: detect-version
-      shell: bash
-      run: |
-        PLAYWRIGHT_VERSION=$(pnpm ls @playwright/test --json | jq --raw-output '.[0].devDependencies["@playwright/test"].version')
-        echo "playwright-version=$PLAYWRIGHT_VERSION" >> $GITHUB_OUTPUT
-
-    - name: Cache Playwright Browsers
-      uses: actions/cache@v4
-      id: cache-playwright-browsers
-      with:
-        path: '~/.cache/ms-playwright'
-        key: ${{ runner.os }}-playwright-browsers-${{ steps.detect-version.outputs.playwright-version }}
-
-    - name: Install Playwright Browsers
-      if: steps.cache-playwright-browsers.outputs.cache-hit != 'true'
-      shell: bash
-      run: pnpm exec playwright install chromium --with-deps
-
-    - name: Install Playwright Browsers (operating system dependencies)
-      if: steps.cache-playwright-browsers.outputs.cache-hit == 'true'
-      shell: bash
-      run: pnpm exec playwright install-deps