I wanted to put my thoughts down somewhere, and here people can say "yeah nah" and poke holes in them.
Of the real dragons, the player character has encountered bahamut*, nidhogg, ratatoskr** midgardsormr, hraesvelgr, tiamat, shinryu***, Vritra and azdaja.
I don't believe vritra nor adzaja(nor fiends/golbez/zeromus) donated aether to the player, so they are unlikely candidates for showing up in the skills. Likewise tiamat only recieved aether when being untempered, so if anything is more likely to get a porxie/alisae themed attack than the WoL getting one of hers. Both Hraesvelgr and Nidhogg's eyes were in close proximity to the WoL, so are the most likely to have had an effect. Midgardsormr, while in close proximity to the player, was greatly weakened and his corpse didn't seem to have eyes so that's a bit odd. Bahamut may be accessible, but seems largely reserved for summoners. Shinryu is a wildcard I think, but after featuring in the climactic fights for two expansions, I could see traits from him being acquired.
Despite meeting most of the first brood too, Estinien is probably "the" nidhogg dragoon. He did have a significantly higher level of exposure to him (his funny turn at 50 job quest, host to two eyes for 3 patches), and hasn't demonstrated any other dragon's traits. Several WoL abilities also seem nidhogg themed, dragonfire dive and rise of the dragon being the most obvious. Also stardiver and nastrond. Despite using the name "gierskogul" in nidhogg's rage, it seems closer to nastrond. Estinien's armour/lance being drenched in nidhogg blood seems to have infused them with nidhogg essence to a degree too, the player probably had a shower instead of keeping it though.
The player also borrows Hraesvelgr's eye for the final steps of faith, who probably is alluded to by the wyrmwind thrust animation and blue/red auras of blood/life of the dragon. BotD was learnt at 54, around when hraesvelgr is encountered. Gierskogul may be more hraesvelgr-themed from colouration, however it's learnt a bit before getting to borrow the eye so doesn't have as strong case.
Ratatoskr - the level 70 artifact armour was blessed or something. It's in a short story I think. I imagine if the player were to eat an ishgardian elezen they'd get trace amounts of exposure this way too.
Midgardsormr I think is only represented in starcross - the "walls" of the jump being similar to the edges of the arena following the intermission in O11. It also has a whiter-than-botd noodle upon impact, so this while this might be hraesvelgr the colour seems off. Rather than being the starcrossed lovers/romeo and juliet/hraesvelgr and ysael angle, it would make sense if the name is a literal "star cross", the activity midgardsormr is known for.
My primary theory until o11 and endwalker really killed it was midgardsormr's true form was some 14 eyed dragon god, with a pair given to each of the first brood. That said, I am starting to wonder again where midgardsormr's eyes went. Maybe hydaelyn needed more juice for the mothercrystal which was both the tithe and how shinryu came back. Either way, I'm surprised at how little impact he seems to have had on the player's skillset.
*a primal but as per the summoner job quests, is still dragon shaped when drawn upon.
** the blood's inside all the ishgard elves, probably the most tenuous but mentioned for completion
*** a primal made fueled by the nidhogg eyes. Probably not really a dragon in its own right, and uses worm rather than wyrm in naming convention.