Only Show the Relevant, but Have the Whole Story:
You have a very complicated world, with LOTS of moving parts that will require tons of explanation. I love worlds like that, but you'll need to consider what you're trying to accomplish with the story. All those hundreds of shiny pieces of information are a draw on your reader's attention. If they're too busy looking at the shiny worldbuilding detail, they won't see Carrie's emotional pain at the death of her cyber-familiar.
So you have the whole world, but only a certain percentage of the stuff REALLY needs explanation. It's enough for now that the bartender is four-armed. It's color. But the really critical point of describing him is as a good listener. The waiter has a cybernetic hand he lights the candles with, but the key issue is that it's a military-grade arm and it reveals he's actually former special forces.
Figure out the central point you want your story to make, and concentrate your details to emphasize those parts. If the magic system is critical to story development, go into the messy details of that at some point (preferably revealed in snippets as the story progresses). Pick a few details to play up, and really explain those, integrating them throughout the story.
But if you have a complex world, and want your readers to fully appreciate all the nuances, you may have to wait for a sequel.