[sgl-router] Book the input_ids forwarding outcome only for built bodies - #41342

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/checkout@v4, dorny/paths-filter@v3. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/

PR is missing the 'run-ci' label; skipping sgl-router tiers. Apply the label to opt in.