To an extent, yes, but they could do it much more easily and accurately if there was a unique, biometric identifier associated with all your actions across your devices which cannot be disabled.

It isn’t even just the government, big tech wants this too. They want to be able to track everything you do with your computer, and that’s more easily achieved if OS level identification is required. Big tech wants it for data harvesting and ad targeting, the government wants it for surveillance and narrative control. The end goal is government verified digital ID that will be required to use any operating system. There will be no anonymity anymore. This creates a panopticon effect in which people police themselves because they know they are always being watched. Furthermore, the information you receive in your social media feeds and web searches can be silently curated based on what is known about your political attitudes. It can all be managed by AI.

It won’t be government supplied. You’ll buy a basic terminal from some big tech company, and then subscribe to a plan that will grant you access to remote processing, memory, and cloud storage. Think Google Stadia but for everything. Using a computer will be more like using, say, the PlayStation store. You won’t be able to install whatever you like - only what is made available. Piracy or adblocking will be impossible. Privacy and anonymity will become things of the past. Even news and information will be curated. And you’ll have to keep paying for it all in perpetuity, while being tracked and forced to consume manipulative, targeted advertising.