ci: run only integration tests in the Integration Tests job, sharded across six runners with per-shard build caches - #1402

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/cache@0057852bfaa89a56745cba8c7296529d2fc39830, nick-fields/retry@ce71cc2ab81d554ebbe88c79ab5975992d79ba08. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/