There is a fan theory circulating around that the people of Fontaine are actually similar to hydro eidolons or oceanids. They can combine form and split like other oceanids. Moreover, that is partly why they dissolve in primordial water whereas non-Fontaine people do not: because the bodies of native Fontaine people are different.
Part of this theory is that Egeria was an oceanid who created the people of Fontaine from her tears and that the Fontaine people are like hydro eidolons, made from Egeria's body. This would explain how Rene and Jakob have bodies similar to the sacred lotus in Sumeru, which is made of Egeria's remains. Moreover, Egeria would have created oceanids before the cataclysm as Rene and Jakob lived before it. Also, Rene discovered how to merge with other beings and split like an oceanid. He was discovering that his own body was like an oceanid's. Later on, Rene would attempt to create one giant oceanid to save Fontaine from the cataclysm.
As the theory goes, during the cataclysm, Egeria split herself, sending her main body to Sumeru to fight the abyss, while also leaving behind a part of herself in the Oratrice and another part as Furina, the figurehead / mascot of Fontaine. As Arlecchino discovers, Furina did not have the hydro gnosis. Some speculate that the gnosis lies with Egeria's consciousness in the Oratrice. If the Oratrice is indeed a kind of liquid form of Egeria's remnant consciousness, then it could explain why it is able to deliver judgements on court cases. Moreover, based on the trial with Childe, it appears that it may have access to knowledge that even Noctis may not be privy to.
In the 3.8 event, it is revealed that the people met in bottleland are hydro eidolons cast in human form acting as people that once met Idiya. Some have pointed out that the event stories in 1.6 and 2.8 serve as an allegorical and symbolic prelude to the subsequent archon quests in Inazuma and Sumeru. So they predict that 3.8 is a prelude to the Fontaine AQ in the sense that the people of Fontaine are like eidolons created from the body of Egeria, similar to how the Melusines are created from the blood cells of the deceased dragon Elynas.
One question this theory raises then is how come when using elemental sight, Fontaine people do not appear blue?
But yet again, if Fontaine people are truly hydro elemental beings, would they not be able to harness the powers of hydro like vision holders, allogenes, or dragons? Could it be that rather than pure elemental beings like hydro eidolons that Fontaine people are actually mixed with other types of energy? After all, there are things like Arkhe and the three realms, including the heavenly energy and abyssal energy that supposedly have a higher 'authority' or 'priority' over the elements.
Recall that Rene and Jakob (composed of Egeria's remains) also experimented with combining abyssal energy.
So it turns out that from the 4.2 AQ, Fontaine people were originally oceanids infused with primordial seawater. After the divine throne of Focalors was destroyed and the elemental authority was restored to Noctis, he turned that primordial seawater into true blood, making the Fontaine people true humans.
Even though humans do have water inside them (biologically in real life humans are composed of 60% water), when using elemental sight, they do not appear blue. So this is just getting a bit pedantic. How come elemental beings like slimes appear blue under elemental sight whereas beings that have some water in them do not appear blue? How does elemental sight even work? Do you have to be like more than 60% water to appear blue? More than 80%? Or is it because humans are mixed with other substances so they are not pure hydro? But even the traveler and other entities (like treasure hoarders) can be afflicted with the hydro element and appear blue. So maybe the surface needs to be affected with water?
Even before Fontaine people were turned into true humans with real blood, they were 'incomplete' humans, not necessarily pure oceanids either as they were mixed with primordial water. So they could be different from hydro eidolons that were just shapeshifting because of this infusion of primordial water.
Regardless, the whole point is that in light of new lore from 4.2, it is not necessarily contradictory that Fontaine people do not appear blue under elemental sight. Perhaps the more important question is what exactly is primordial water, how is it different from regular water, does it have any connection to the realm of celestia or the abyss? What is it that gives it its life-granting properties?