Removes check-changes and reorders jobs

[jasonb5]

Removes check-changes since the triggers are filter by
paths. Runs the cleanup job first, to prevent the new commit
from cancelling existing doc deployment workflow.

Test suite: n/a
Test baseline: n/a
Test namelist changes: n/a
Test status: n/a

Fixes n/a
User interface changes?: N
Update gh-pages html (Y/N)?: Y

[github-actions]

You can preview documentation at https://esmci.github.io/cime/branch/fix_doc_deploy/html/index.html