hitl public endpoint refactoring

[Lee-W]

Body

As Brent suggested, we no longer need to follow the old convention. Thus, we can merge those HITL non-mapped/mapped endpoints into one

Committer

• I acknowledge that I am a maintainer/committer of the Apache Airflow project.

[Lee-W]

@guan404ming, as we just discussed. But this is super low priority. So let me know if you're no longer interested in this one or don't have the bandwidth to do it. Thanks 😄

[Lee-W]

completed by @guan404ming through #54723