You already got to that in your question:
Or is the meaning of the Actor feat that they only have advantage when they are trying to prove that they are a different person not in other situations?
That’s exactly it. Actor gives you advantage on deception and performance checks that you incur from trying to pretend that you’re a different person. It doesn’t apply to other things you happen to be doing while passing yourself off as another person.
This paragraph from the question also isn’t quite correct:
So basically, as long as the person you are changing into is/ was a real person, you are always passing yourself off as a different person.
Not necessarily. You’re just changing your appearance to look like that person. But you might not necessarily actually pretend to be that person. Maybe you’re just showing off your shapeshifting ability as a party trick. Also, Actor doesn’t require that you pass yourself off as a different real person at all; It’s perfectly within the bounds of it to try to pretend to be some made up person like a traveling noble or what not, although of course with shapeshifting and incredible acting skills it’ll be quite beneficial to you if you can find a real person to imitate.
Really curious if this is kinda broken because a bard or rogue with expertise and advantage on all deception checks could be a crazy good liar.
I’d also like to address this point: Advantage or not, a Bard or Rogue – especially the Rogue, because of Reliable Talent – with Expertise in Deception are crazy good liars. So good in fact that they’ll rarely ever fail a deception check for anything that isn’t a completely outlandish claim, advantage or not. This isn’t a problem. They built their characters to be good at something, so they get to be good at that thing.