Ensure that generated documentation gets merged into website automatically (etcd-io/website)

As per the discussion in the [March 11, 2021 etcd public meeting](https://docs.google.com/document/d/16XEGyPBisZvmmoIHSZzv__LoyOeluC5a4x353CX0SIM/edit#heading=h.2pcfcuck4vc), we need to ensure that generated documentation gets merged into website automatically on update.

Opening an issue in the website repo as well in case we need to make any changes here as well.

Related issues:
* etcd-io/etcd companion to this issue: Ensure that generated documentation gets merged into website automatically [#12768](https://github.com/etcd-io/etcd/issues/12768)
* Etcd.io Docs/SEO Improvement Plan [#65](https://github.com/etcd-io/website/issues/65)

/cc @hexfusion, @ptabor, @spzala