This is a limitation with the job framework in Prime Infrastructure. Essentially, once a job trigger has lapsed, it will be expired and any approval will be too late. In 3.2, if my memory serves, all of the jobs we create are executed nearly instantaneously, which leaves no opportunity for meaningful approval. So that's why the API job types don't appear in the list.
I've talked to the job framework team about this, and they've agreed that it is a problematic limitation, but changes haven't been implemented yet. We've also had some internal discussion about job approval API resources; however, there are two things that we need to address first. One is that the job framework has some technical limitations that would make an API-based workflow on job approval difficult. The other is that this limitation with job approval should be addressed as well, so we can have a 100% API-based workflow around this.
I'll reach out to my colleagues in the job framework team again, citing this post. Probably not the answers you wanted, but I hope that clarifies things.