How has the Golden Company managed to keep a hold on Blackfyre this long? Surely Haegon, and Daemon III would have been fighting with it when they were killed. For that matter, how do you think the Company got out of Westeros in one piece after Wendwater Bridge or the final defeat of the Third Blackfyre Rebellion?

There are major open questions there. In terms of the sword, it’s probable that the same “friends at court” who freed Bittersteel after Haegon’s murder also liberated the sword. Given how close to their original landing the Fourth Rebellion ended, it’s quite likely that Bittersteel simply just retreated back to the boats with the sword.

As to the army, that’s quite curious. Obviously, the Golden Company’s discipline helps a good deal in terms of keeping the army together in retreat, especially with Bittersteel being captive in the aftermath of the Third Rebellion. Most likely, they retreated back to their Tyroshi fleet at some rendezvous point. 

But honestly we don’t know enough about the course of either war to be sure.