I would also note that in 1500 posts it has not yet been discussed whether everyone is using the same definition of the word "rule". Arguing about whether or not something meets a definition without first establishing that definition seems doomed to be inherently unresolvable.
From my standpoint it seems highly likely that everyone who has expressed an opinion on whether or not it's a rule is simultaneously correct, under whatever definition of "rule" they happen to be using.
There is different kinds of rules. You got mechanical rules, AKA rules of the game, and narrative rules, AKA rules of the world.
Mechanical rules are usually used to express the rules of the world, but they can be arbitrary to simply evoke a specific theme or flavor. Sometimes a mechanical rule gets a fluff explanation after the fact, sometimes a fluff explanation gets a rule afterward. Unarmored defense was given to the Barbarian so they can stay shirtless and not be hit all the time. It reinforces the theme and it explains a piece of the fluff. A player can break a rule and that would be cheating in our world.
But you also have rules IN UNIVERSE. Like the law of a town your characters visit. If the character choose, of their own free will, to break the law of the town, then the town will want to deal out justice. The player is not breaking any rule of the game, just because the character is.
I would also argue that there are, in a game, meta rules. Rules that exist for the same of understanding rules. Keywords, for exemple, are a meta rule. Same as using icons to represent certain mechanics. Those meta rules also extend into game design. It's not something that's easy to list out, but there are principles to adhere to if you want to make the rules of your game understandable and easy to learn. One of which is consistency: things that are worded the same mean the same thing and things that are worded using other words mean another thing.
"Will not wear metal armor" break those game design principles. It doesn't follow 5e's meta rules of how rules are expressed.
D&D is generally described as a "do anything you want!" game where the limit is your imagination, and it is true... but the game offers you multiple types of resolution mechanics and suggest you either try to resolve situations through those mechanic, or use them as inspiration for your own solutions. Despite placing limits on what you can and can't do, 5e's rules are usually expressed in a permissive format: "You can do X", "You do X to do Y", "You can do X if you do Y", "You can cast X", "You know how to use X". They do not list what you cannot do, and will usually list what happens if you try to do something you have not been granted permission to do (say, use armor or weapons without proficiency).
In fact, I don't know ANY modern game, RPG or board games, that uses "Will not" in its rule text outside describing the way an NPC would act, usually in regard to what a PC can ask them to do, or an automata in a solo mode board game. An NPC, not a player, because human players are assumed to have free will and that free will extends to their characters.
When rules of the universe, rules that can be broken (not gravity or the innate capabilities of a dragon) mind you, are explained, they ALWAYS include some kind of in-universe consequences, and sometimes they'll even include explanations of why things are as they are. Because the basic mechanical rule of D&D is that you can try to do 'anything you want' and all the other rules exist to see if you achieve your goal or not. You character CAN break the law of the town by robbing them blind - D&D assumes as a default that PCs have free will - but the consequences are narrative and not mechanical.
"Will not wear metal armor" also break with that concept, in that it offers no consequences, no lore reason why things are as they are, no elaboration.
"Will not wear metal armor" breaks the meta rules of 5e. It is not formulated or formaed like either a mechanical rule or a in-universe rule, as a result it does not function as a rule as is. It cannot be, for me at least, a rule of any kind. It is, at best, a programming mistake that needs to be patched to work properly and DMs are left to their our devices, should it come up, to solve this glitch.