This improvement aims to enhance the RebuildLiveWorkspaceComponent API to add a rebuildLive(Site) method which (re)build the live of a site. Thus the component is being renamed into RebuildLiveComponent and existing rebuild actions/tasks are updated to reflect the changes.
This allows us to use the RebuildLiveComponent to rebuild the site wherever needed (and not only in the BuildLiveAction.

A patch proposal is attached to the issue.