Some of the questions here are really difficult to answer and I'm struggling a bit with them too.
Why is Johnny's engram on the relic? I think I have a good theory as to why Arasaka kept Johnny's engram in the first place, but not how he came to be on the relic. Its likely they kept him for intelligence extraction at the end of the 4th corporate war. Since the nuclear attack on Arasaka Tower was a Militech black op, they were hoping to find something that ties Johnny to Militech in order to justify a retaliatory strike, which would either extend the 4th corporate war or start a 5th one. But I don't think Johnny knew shit based on his recollection of the events in the game.
It also makes sense that he would never knowingly work for Militech in one of their black ops. Militech likewise is happy for Johnny to take the blame for the domestic terror attack. They create a pretext to expel Arasaka from the continental US and start an asset grab under the guise of national security. We know that Militech were temporarily re-nationalized by the US government at that time.
Megacorps are well resourced enough that they can contract out wetwork and leave no traces - no money trails, no recorded communications, nothing that leads back to the corp. This also explains why Johnny doesn't remember anything about Morgan Blackhand, given that he created Johnny's "distraction team" and is a de facto Militech employee. Its probable Johnny didn't even know he was involved either. I think Johnny was a useful pawn in a megacorp power play he didn't understand, but Arasaka didn't know that.
So they tried to get actionable intelligence out of him at the end of the 4th corporate, don't find anything, shelved him indefinitely, then forget about him. So who takes him out of the archives to put him on the relic? Was it Helman? Maybe I missed something but it doesnt make sense. The second protype was a personal project of Saburo's and was intended for him. The only thing I can come up with by way of explanation is the second prototype was going to go into a trial phase where they use it on a guinea pig. And Saburo would talk to the guinea pig and would know the trial had been successful if he recognised the mind of an old adversary. But ultimately Johnny is inconsequential and I don't think Saburo ever thought of him as a real adversary, so it feels a bit thin.
Was it Yorinobu? He stole the relic but if he had planned to overwrite Saburo's mind with Johnny's engram, he wouldn't have strangled his father at Konpeki. Or if he did, he would have slotted the relic into his father's head, bringing back from the brink of death, made up with the family and rejoined the fold. Then he would have watched as the iconic head of Arasaka corp slowly started getting real funky anti corpo ideas and some killer guitar licks...
So if Yorinobu stole the relic, why would he sell it to Netwatch? Netwatch is like a neutral organisation funded by megacorps, so while they have megacorp infosec as their mandate (broadly speaking), I don't think they would want to be involved with inter corp conflict. Thats not their purpose and they have nothing to gain by inserting themselves in the middle of it.
How does Brigitte know that Johnny's engram is on the relic? Don't know. She needs it to break through the blackwall but again, we come back to the frustrating question of who put Johnny on the relic? VBDs are some of the most highly skilled runners around so its possible they stole this intel? Maybe? That would mean Brigitte orchestrated the heist though right?