Seems like they're preparing a new part of Time Temple.

we can already travel to the past if i am not wrong, ellin forest, however, the door to the past in the ToT takes us to our past memories if i remember correctly.

I actually think that the Door to the Past does take us back in time.
It would make sense if Pink Bean's summoning was a long-ago attempt at bringing back the Black Mage since the Black Wings don't seem involved in it at all.

I was reading the quest log data and I'm not sure if this quest comes after defeating Cygnus, but basically Shinsoo has a quest for you and says "This is not the future" and to meet up with him in present time. Then, "You learned that the Gate to the Future actually leads to a dream world created by the Black Mage.
Return to the Black Mage's dream world and search for some clue as to the Black Mage's identity."
Shinsoo then says to defeat Cygnus again. You then find a Dream Fragment and talk to Athena (present time) about it, who has no clue about it and is acting strange. So you go to Neinheart in present time.
"You've learned that the Black Mage has a follower who can create and manipulate dreams. This Dream Fragment might be related, but...why was it in the future?"

And that's pretty much it ( I think)

That actually makes a lot of sense because, when you get your first Dream Fragment, you're told to take it to Neinhert.
I don't remember the text verbatim, but he definitely makes it sound like Dream Fragments are the remains of something that has been conjured up.

Of course, if the rest of what you say is true, it makes me wonder what the point of the Dream World is.
If it's not real, it's not a threat unless someone goes in it or something comes out of it.

Remember the Evan/Aran storylines about the pink crystals that sealed away the Black Mage? Whatever happened to that?
I'd like to think they'd pick it up again, or make something based on it...

I hope those MacGuffins get retconned out or retconned into something else.
The entire time I was doing those quests I kept thinking, "Oh, there's a set of mystical stones that are scattered because, if they're brought back together, they can free the Black Mage. Where have I heard that before?"

Every time a work of fiction has a sealed baddie who can be freed by a formula created by those who sealed him, I facedesk.