*cracks knuckles* OKAY
(and before i start im so sorry if this was some sort of meme poll. unfortunately i genuinely cannot tell right now)
SO. i have thought long and hard about this. firstly, it's important to note that secret stones do not grant you mastery of any powers nor does it grant you any new powers. i'm pretty sure that's what mineru said. no, i DONT know how to explain the avatars if this is the case, aside from them being some sort of projection of the sages that has very little to do with their magic? idk how to explain it.
BUT
i think that link's sage title could boil down to 3 things.
- time: this one i think is the most possible. i know that zelda is the sage of time in canon, but let's just pretend this is a roleswap. link canonically has abilities to manipulate the passage of time around him, which is commented on by both daruk (in his training journal) and teba. link said to daruk that it feels like time slows down around him when he focuses. in game, this manifests as bullet time and flurry rushes (fun fact: in totk, stamina in bullet time is only used when you fire an arrow whereas in botw, its time-based. i like to think that this is link slowly mastering his own powers between botw and totk). additionally, zelda grants link one of her own abilities (recall) at the beginning of the game. this is more of her vow than anything else, but it's a unique one, like mineru's vow is.
- spirit: this one i don't have a ton of in-game evidence for, aside from link collecting the poes for the collector. in canon, he's freed several spirits. in totk, it could be that the ancient sages are talking directly to their descendents, and link happens to hear them as well. buliara can't hear the ancient gerudo sage, but link can, and ofc riju can. once you get to mineru, she's immediately more clear and can say more to link. he can only hear the other ancient sages say a few words at first, or nothing at all. i like to think he's more spiritually sensitive than most other people in hyrule, although the spirits with green flames around them are visible to everyone (yunobo can see daruk standing on top of vah rudania after link frees it)
- light: this here is more of a narrative choice. link has rauru's arm, and the master sword, which is said to be infused with divine light (and it is, as per sksw). this one, i think, is more of a weaker argument though since link doesn't actually have any light magic abilities. that would be zelda.
(there's also a super secret shadow option if you headcanon link as having sheikah heritage and being trained as a sheikah pre-calamity, but that's more of a thing for an au than based in anything canon)