That Link from the Skyward Sword Manga is Canon and the true first incarnation of Link.
Fierce Deity Link is actually Link taking on the role as the God of Time. Since Hylia sacrificed her Divinity to live as a mortal and her bloodline carries her powers, her throne as the Goddess of Time was vacant. So since Link's soul was given eternal life through reincarnation, his soul is now bound to time itself. So when Link dons the Fierce Deity Mask, he assumes his full potential power-scale as it is him taking his full Divine form. This would also explain as to why when OoT Link abandoned the Adulthood Timeline, his soul was still able to reincarnate into the Hero of Winds from The Wind Waker and Phantom Hourglass; since his soul itself is bound to time itself and he is for all intents and purposes the God of Time.
Hyrule Warriors is Canon, but it takes place far down the timelines, so far down that it is in the Reunified Timeline and possibly 1,000 years before the events of Breath of the Wild's 10,000 Prologue period.
Also, considering how powerful Link gets in each game (20 Hearts), then suddenly finds himself in his next adventure with just 3 Hearts; i think it shows just how MUCH HIGHER the stakes are. OoT Link essentially has 40 Hearts after being blessed by one of the Great Fairies. But in Majora's Mask he suddenly has 3 Hearts again. Which means that when he gets to the end with 20 Hearts and that Newer blessing to bring him up to 40 Hearts worth of strength again with that damage resistance, that would technically make him have ... 532 OoT hearts by the end of Majora's Mask.
Which means that given that ALttP Link, who has 4 adventures under his belt, is likely the MOST POWERFUL LINK TO EXIST EVER
And to add in an edit -
The Royal Family is kinda dumb. Every time the Spirit of the Hero is born, his parents are compelled to name him Link. So this means that every year the Royal Family SHOULD do a census and learn WHO is named Link and THEN force them to train as a knight so that they can guarantee that the Spirit of the Hero is prepped and ready as possible for the coming crisis.
This could be useful as an amazing plot point, as there could be multiple characters in a Zelda game named Link, performing heroic deeds and only YOU the player are the correct Link. So this could spark some rivalries and possibly make the game's antagonist BE one of the Links who feels hatred and scorn for being told he was destined for greatness only for the twink Link to be the one declared the chosen hero by the gods!