Most computers in the anarchy zone future history use trinary logic - that is 0/.5/1 rather than only 0/1 binary. Many are also base around optical hardware, and some even quantum. However, very few people use computers. Those are just machines that sit in the other room, bouncing around lasers to to read data. What people use is their shirt sleeves and glasses.
The Sphere is not the internet. The Sphere is augmented reality. Through either glasses, contacts, or even optical implants, people can see Elements of the grid. By way of analogy imagine everything in the world covered with bulletin boards, and the ability of everyone to post notes as they see fit, and sort through those of friends or some select group of strangers. Directions to an unfamiliar restaurant are given by a virtual line running though the streets rather than a sequence of names and turning directions.
Buttons integrated into sleeves, armbands, or other articles of clothing mean most tasks don't require pulling out a device - just tapping on your non-dominant limb. Although there is some gesture and voice recognition - these are generally reserved for private settings where cross signals from others won't be a problem, and the user's movement won't disturb bystanders. Folding keyboards and tablets offer another input option.
Some people still use the internet as a early 20th century user might recognize it. An old binary based architecture still kept for those with nostalgia or nefarious purposes in mind.
Post Event Sphere
The Event was heralded by a massive electromagnetic pulse/solar flare phenomenon. Optical or not, computers still need electricity - so the shut down of power grinds across the planet rendered most of them non functional. Those who can get a server working have an excellent resource for storing data or providing assistance over a limited area. However, given the bandwidth of transmissions required - signals don't broadcast far without the cellular repeater network - so setting up new systems in the immediate are is necessary to get the most use out of the thing.