Thus per the definition, Satoshi's PoW design is not Byzantine fault tolerant, because the metric of when it is fault tolerant is ill defined (can't be measured). An unknowable state is as reliable (fault tolerant) and a random result, thus no reliability exists.
This is exactly the same as the Byzantine Generals Problem, which is solved up to 1/3 faulty generals (and only then, unless you add externally-assigned identities and unforgeable messages). If there are >1/3 faulty generals, then the honest generals
can not determine that they are being tricked, so they will commence a doomed attack and they will all die. This is fault tolerant
up to 1/3 traitor generals but not beyond. There is no way for the honest Generals to measure the number of traitor generals. If they could, they would not be tricked into attacking and die.
Likewise, in Bitcoin if there is <50%* faulty hash rate, then there is no effective censorship and functional consensus (including on there being no effective censorship). If there is too much faulty hash rate, then the rest of the system can not measure the faulty hash rate and it can not determine that it is being tricked.
In both cases, an outside observer who is able to see all the interactions can tell the system has failed. Within the system you can not.
That is the statement of the problem. The problem is not fault tolerant!
The only fault tolerant design for a solution is with centralization which obviously doesn't address the requirements of the problem, .e.g as you say "unless you add externally-assigned identities and unforgeable messages".
Thus I wrote upthread there is no solution to BGP. The problem will never be solved as stated.