Again, the spirits literally come from a spirit world and described in-universe as supernatural. That's why the Avatar exists: the bridge the two.
This is overthinking it to an extreme.
The litmus test is whether the setting considers an element supernatural, not what we think about it personally.
Most settings consider it to be an ancient magic. Spellwright by Blake Charlton comes close to your question by having writing another language be the core of it's spellcasting system, so yes, speaking another language can be supernatural.
Now you're going the other direction where you're saying 'natural' means 'existing'.
I mean, natural in terms of our real world IS existing. Quasars sending gamma pulses through the potential infinity of space is grand and epic... and they exist and are therefore natural.
I won't deny this is a bit of overthinking, but it comes with a purpose. For example talking to a fire spirit in the language of fire is supernatural in the Spellwright series you just mentioned, but is speaking to a magma mephit in Ignan supernatural in DnD? I've read stories where a wizard is merely someone who makes deals with spirits, and the spirits do the effects, such as how Shintoism handles it. Would it then be supernatural to speak to the fey and have them use their magic? That is how a wizard works in that setting?
I don't particularly think the definition matters, we don't need this to be answered, to actually move forward with making abilities, but it does start to show the problem with using the word only as the people in the setting might use it. Especially since, the words used by the setting are the words WE use for it.
In DnD, no one would find it supernatural to make a healing potion, or to learn wizardry, or at least no one would find those any more supernatural than we find medicinal teas and engineers. Yet, the effect they have is clearly meant to invoke magic and the supernatural. And what of Sci-Fi? Fate Manipulators exist in Sci-Fi, and many times they are presented as though what they are doing is mere technology and knowledge, but in a fantasy setting, that would be considered supernatural. If I wanted to port these things into a game... which term should I use?
And, the best part about having supernatural be from the perspective of the readership/players is that there can be no debate about it. You cannot truly debate if wizardry in DnD is supernatural or natural if you are taking the position of the reader looking in, because no one in our world can summon creatures through portals or form ice out of thin air with mere words and gestures. It is a clear, easily defined, and consistent line. Is it possible IRL? Y/N. Meanwhile, if you take it from "is this supernatural in terms of the world" then you could have one person lighting their fists on fire, and that is entirely natural, and the other person lighting their fists on fire being supernatural. Which is weird, and not helpful for defining the abilities.
