I think of the government part as largely an accident; my definition of fiat money is “money that has value solely because the transacting parties say it has, and not intrinsic uses” - historically the way to get people to agree something intrinsically value-less has value was by government decree, but there are lots of exceptions. I think of the Yapannese rei stones as fiat money, for example (though there is some question about them having inherent value). Basically any money that isn’t commodity money (or directly redeemable for commodities) is a fiat money.
I think your definition is faulty: are you aware of shell money? This served as money enabling international trade for thousands of years[1], and can you say these shells have intrinsic uses?[2] These shells had value because of their properties: compact, scarce, unforgeable.
In contrast, fiat value is held because an authoritative party says value is held, e.g. Chucky Cheese tokens, or the USD. Fiat requires this authority, as in its definition: “An arbitrary order or decree.”
There are no authoritative parties declaring that Bitcoin has value, rather the market is arriving at that conclusion through decentralized operation, just as has occurred for thousands of years with gold, shells, etc.
Shell money began as commodity money according to most sources- shells were inherently valuable because of body ornamentation as you mention (similar to how gold was useful to easily work into soft metal jewelry).
If Chucky cheese tokens are money at all, they are “representative money” because they can be readily exchanged for various commodities by the issuer (the prizes and games).
A central authorities decree is not required for money to be fiat, it just simply can’t have intrinsic uses like commodity money or be directly redeemable for commodities like representative money. It has value purely because we have confidence it will have value in the future - and historically the most reliable way to do that is by government decree, but it could also be by a mass consensus that a particular crypto coin will still be used in the future.
I expect economics textbooks in the future will refer to this time as the time this question was settled: were shells and gold money because of their intrinsic ability to be used as jewelry etc., or was it jewelry because their other properties (particularly scarcity / unforgeable costliness) made them natural monies?
Hard money advocates have been arguing this point recently, and IMO it can only be settled by the market and observation. Only if the latter is true, does Bitcoin have a valid claim to become money.
https://en.m.wikipedia.org/wiki/Fiat_money