When someone asks a question but actually just want to answer it themselves [duplicate]

A question like that is a “prompt”. From the Online Oxford Dictionary:

An act of encouraging a hesitating speaker. ‘with barely a prompt, Barbara talked on’

The kind of question that is designed to elicit a known answer for the audience's benefit is neither rhetorical, leading, nor loaded.

It's a guiding question designed to elicit answers that tell a story. This is a partly scripted interview (the interviewer knows the expected answer and has the next question ready).

See, for example, this article on doing a television interview.

Another type of question is the open-ended question, often designed to elicit emotional response.