Closes#15129
Adds a generated **Beta features** table on the feature stages doc,
using the same mainline/stable sparse-checkout approach as the
early-access experiments list.
- Walk `docs/manifest.json` for routes with `state: ["beta"]` and render
a table (title, description, mainline vs stable).
- Inject output between `<!-- BEGIN: available-beta-features -->` /
`END` in `docs/install/releases/feature-stages.md`.
- Rename `scripts/release/docs_update_experiments.sh` →
`docs_update_feature_stages.sh`, refresh the script header, and use
`build/docs/feature-stages` for clone output.
<img width="1624" height="1061" alt="image"
src="https://github.com/user-attachments/assets/5fa811dd-9b80-446b-ae65-ec6e6cfedd6a"
/>
Jake Howell
8f73e46c2f