fix(site): use a new file for every www check - #517

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/cache@v4, actions/checkout@v2. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/

The `set-output` command is deprecated and will be disabled soon. Please upgrade to using Environment Files. For more information see: https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/