Tense and Aspect – Differences Between ‘Has Started Taking’, ‘Has Been Taking’, ‘Has Taken’, and ‘Took’

For all practical purposes, there's really not much difference in meaning. Either one could be used to announce the appointment of a new manager.

Let's assume we appoint Renee as the manager today. Our Regional Director comes into the office to make the announcement:

Renee is appointed as Manager.

Tomorrow, an absent co-worker comes into work, and asks:

Who was appointed Manager?

(This co-worker uses the past tense, because the appointment happened yesterday). I might reply:

Renee has been appointed has manager.

So, why didn't I say, "Renee was appointed as the manager" instead? Because Renee is still the manager! I could use was – it wouldn't be incorrect – but it might lead to some confusion. I can imagine my co-worker saying:

Was? What do you mean, "was"? Isn't Renee still the manager?

The further the event moves into the past, though, the more natural was will sound, because we're talking about an historical event, rather than a current event. Imagine we fast-forward two years into the future, and I am training a brand-new employee:

Tracy was our manager until two years ago, but then he retired.
Oh, then what happened?
Then Renee was appointed as Manager.

Renee's appointment is no longer a current event, so "has been" doesn't sound right in that context.

This looks a lot like the present perfect continuous tense, except that tense uses a verb that ends with -ing:

Our company president has been appointing a lot of hot shots with very little experience.

I'm don't think your sentence is quite the same thing, though, because of how we'd parse your original sentence. It's not:

Renee (has been) (appointed) (as Manager).

but:

Renee (has) (been appointed) (as Manager).

So, we're really dealing with passive voice here, not the present perfect continuous tense. In active voice, we would say:

The company president has appointed Renee as Manager.

or, the Regional Director might say:

We have appointed Renee as Manager.

Don't be so hard on yourself. English is very difficult.

This talks about present perfect tense - which have been by itself falls under, and have been by itself can be used to describe an experience:

You can use the Present Perfect to describe your experience. It is like saying, "I have the experience of..." You can also use this tense to say that you have never had a certain experience. The Present Perfect is NOT used to describe a specific event.

Have been + {-ing form of verb} is present perfect continuous tense, which is different. That's used to talk about something that has started at some time in the past and is still ongoing or happening now.

Putting would in front of either of these now says that the action or experience did not happen because of something. Typically a clause will precede or follow explaining why, typically starting with but.

I would have been to Japan, but I was unable to afford the trip.

I hated her guts. I would have otherwise gone to the skating rink.

I would have been going with him, but he sort of creeped me out. So I went with her instead.

We would have ruled the entire kingdom, yet their relentless attacks on our land proved it impossible.