- Rename the workflow into `publish-module-api-doc` to be consistent
  with other workflow names.
- Refactor workflow triggers.
- Run the workflow only on push to the tarantool/tarantool repository
  or on pull request if the 'notest' label is not set.
- Simplify condition for publishing generated API documentation.

NO_DOC=ci
NO_TEST=ci
NO_CHANGELOG=ci

(cherry picked from commit c9e0074d)