I'm super grateful for you taking the time to give such a detailed answer. Stories are often up for interpretation, but I can provide what my intention was at least to the story.
The three divisions are all working on seperate projects. Newminds are making the AI powering the robots (and are responsible for most of the obstacle course like rooms) Interface is developing brain-computer interfaces, and Everlight is trying to create an immortality device.
Everlight already have a device that can freeze all living matter in place, and they believe that they will be able to localise the stasis to individual cells, allowing people to still get about without aging. As they spend longer and longer without being able to crack cell localisation and David gets sicker and sicker, he eventually starts fudging numbers in desperation, and takes the device to a remote area hoping he'll be able to hold just himself in stasis until a cure is found. Unfortunately, the field is much bigger than he expects and the entire facility is affected. (the room btw is the robot storage room, I like to think every time you die it sucks one of those robots up the tube to place at the checkpoint doors)
The voice that you hear throughout the game is Brian, the scientist who just happened to be testing the Interface device when the stasis field started. (He's in the bottom left of the map)
Like I said, this was something I'm experimenting with, with a view to tell a story similarly in the current non jam game I'm working on, so I really appreciate your feedback.