Programatically sync feature gate status from k/k to documentation

It is a lot of manual effort and error prone to check feature gate stage changes and ensure they are well reflected in the documentation. Feature owners sometimes forget, we sometimes have typos, and there is a non-zero chance for inaccuracies to slip into the website.

Without touching prior feature gates, we should be able to sync the feature gates emitted from k/k's [versioned_feature_list.yaml](https://github.com/kubernetes/kubernetes/blob/master/test/compatibility_lifecycle/reference/versioned_feature_list.yaml) to the [website feature gate status](https://github.com/kubernetes/website/tree/main/content/en/docs/reference/command-line-tools-reference/feature-gates) directory.

Is this something we can leverage scripting for? I see we have a python script `update-imported-docs.py` that does something similar with OpenAPI. Can we add a new script somewhere to mirror the gates in `versioned_feature_list.yaml` in a release (or master) branch into the feature gate directory?

Would https://github.com/kubernetes/kubernetes/issues/128241 be a prerequisite or can we directory use the yaml file?

/cc @lmktfy @tengqm