Refactor build-handbook job to handbook-build-and-deploy

What does this MR do?

Refactor build-handbook job to multiple versions of a handbook-build-and-deploy job, to leverage above changes and do a partial deploy of handbook as part of the job. This will serve as a template/example for continuing to refactor PartialBuild into individual jobs.

Why does there need to be multiple versions of the job? Because in the case of the deploy-cleanup-old-deleted-files jobs, the scheduled pipeline version must still obtain all the artifacts to deploy with the rsync deletion flag. However, that version of the pipeline shouldn't attempt to do a deploy, thus we still need a build-only version of the handbook build jobs.

Note that since this makes the handbook build job longer, it will slightly increase the overall build time. However, this is a temporary issue - once all the other PartialBuild jobs are moved to this same build-and-deploy approach, they will all be independent and not need to wait on each other, and the final deploy job can be deleted.

We can also look into parallelizing the individual jobs in the future too, if performance is still a problem after they are all split up.

Related issues

Relates #8302 (closed)