ALBW Prologue Translated:
There is a legend oft told in Hyrule Kingdom.

It is the legend of the Triforce, once kept within Hyrule itself.
(At this point in the timeline, this could either be referring to the era right after Skyward Sword, or to the era between Oracles of Seasons/Ages and ALBW. The former is more likely because this prologue is supposed to be retelling the events of the Imprisoning War and AttP)

Said to be a gift of the gods, the Triforce could grant a wish of all those who touched it.

So of course, many wanted to get their hands on it. Wars were fought for the Triforce.
(Wars over the Triforce, that could refer to the wars during the Era of Chaos, the Hyrulean Civil War, or to the Imprisoning War)

The royal family summoned the Seven Sages, who sealed the Triforce in the Sacred Realm.
(This part can only be true if it's referring to when the Seven Sages from OoT resealed the Triforce and Ganon during the Imprisoning War in the prologue of AttP. This is because when the Triforce was originally sealed during the Era of Chaos, Hyrule Historia makes no mention of the Seven Sages besides Rauru. As well as the fact when Rauru sealed the Triforce in the Sacred Realm, Hyrule and it's Royal Family had not been established yet. Therefore for this to be true, it'd have to be referring to the events of the Imprisoning War)

But a thief of notorious repute broke into the Sacred Realm and claimed the Triforce.
(This refers to the events of Ocarina of Time when Ganondorf broke into the Sacred Realm. However this makes the previous part impossible because Ganondorf couldn't have broken into the Sacred Realm after it was sealed at the Royal Family's request. Because the Royal Family ordering it to be sealed again was a result of Ganondorf breaking into the Sacred Realm in the first place.

With its power, he became the Demon King Ganon, who sought to dominate all Hyrule.
 (For the previous and this to have any connection, this would have to be referring to the 7 years when Ganondorf ruled Hyrule during OoT and the time after he killed the Hero of Time but before the Imprisoning War)

But just as Ganon had the kingdom in his evil clutches...

a legendary hero answered the call of Hyrule's princess.

And this here, wielding the Master Sword, took up a quest to challenge Ganon's might.

He joined with the descendants of the Seven Sages to seal the Demon King in darkness.
(This cements that the Hero being spoke of here is the Hero from AttP. Because the Hero of Time from OoT lost to Ganon, thus prompting the Imprisoning War. Also if this were still referring to OoT, I'd be the Seven Sages that sealed Ganon, not the descendants. The descendants sealed him in AttP)

The Triforce was divided into three - its tempting power out of any one person's reach.
(This happened in an era between Oracles of Season/Ages and ALBW. Because the Triforce was whole at the end of AttP and the Oracleg games)

One part stayed with the royal family, while another slipped into Ganon's possession.

Legend says that the third part found its home in the heart of the hero eternal...

And while legends come to us from the distant past, others have yet to be written...

So in conclusion, the prologue from ALBW worlds is trying to tell the events of AttP, yet at the same time including elements from Ocarina of Time where they don't belong thus making the backstory convoluted and inaccurate.