Browsers are something the end-user installs. Inserting the government into that doesn't make sense.
This sounds like the idea is for the site to add extra metadata that's not there now, about what each cookie does. Which would still involve mandating site owners to do things.
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Also, both private mode and https://addons.mozilla.org/en-US/firefox/addon/multi-account... are a thing already, without government meddling.