Is your feature request related to a problem? Please describe.

The site.yml workflow is currently triggered in the following scenarios:

1. A push to the main branch, using the state of the site and the workflow as on main.
2. A push to a release/*branch, using the state of the site and the workflow as on that release branch.

Notice that workflows get the repo state (from the checkout actions) and the workflow state as its on that particular branch.
Put in other words: if we'd have a change to some old release/1.0.x branch, the web site would be updated as it is defined on that release/1.0.x branch, which is wrong and not the intended behavior.

Therefore, changes to the versioned-docs branch do not trigger the website publication, because the workflow that does this, the site workflow, is on the main branch.
Simply speaking: a push to versioned-docs doesn't trigger any workflow, because from that branch's perspective, there is just no workflow.

I'll come up with a PR to fix the triggers of the site workflow and in parallel work on a solution to get the website pushed when a push to the versioned-docs branch happens. The latter is a bit more complicated and security implications need to be considered.

Describe the solution you'd like

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Describe alternatives you've considered

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Additional context

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