I thought GDPR regulated the cookies that websites are allowed to request to store on users devices. Does it also cover tracking built into browsers by Google, Microsoft, etc.?
How would the browser discern between legitimate 1st part cookies and illegal privacy violating ones? It's not a technical problem, it needs laws.
And for GDPR and other privacy rules, cookies aren't even a thing. The laws doesn't care about the medium you use. They apply beyond technicalities. For instance you could track IP addresses and a browser would have no way to stop you. GDPR makes it illegal without involving new crazy tech.
GDPR and those data processing consent flows are about data collection and processing in general and not a specific technical means of doing so - it would also apply to IP addresses, browser fingerprinting, information manually entered (such as delivery address when placing an e-commerce order) or a hypothetical crystal ball that actually worked.