I mostly agree with you about Essence - certainly the thematic side of it is not appropriate out of context. It does, however, serve its purpose in Shadowrun mechanically, which is to provide a limiter on bionics without direct appeal to complex biology. It is in that regard that I think it might be useful here, but I may end up doing away with it and using only locational space, rather than an extra Essence limit for hard-to-mathematize bionics.
I see all the calculations and variables as taking place on the design side, not the code side. The game version would see only a location/s and a number of slot points.
Bionics are installed via Compact Bionics Module, which is described as a mostly-automated surgical installer. This is why they have such large volume, even though the bionic itself is tiny. The only role the player has is making sure that the automation is guided appropriately by a human intelligence. I see the fact that players can get CBMs by butchering monsters who have bionics installed is an oversight, or more likely an incomplete feature - presumably the player should be able to build CBMs out of a salvaged bionic and an installer kit of the appropriate level, or install non-module bionics with a team of robo-surgeons at a hospital as you described. If that was the case, they would indeed need a volume and a weight, since each bionic would have to have a representation in the game without its Module.