How does countries keep track of people when they get a new passport?

In my country (Sweden), my passport number is unique to that specific document. When I renew my passport I get a new passport number. I’m guessing this is how it works in most (all?) countries.

But countries still have to keep track of the actual foreign individuals that enter their country. How do they do that? It seems absurd that one would be able to get a “clean slate” by just renewing their passport, and their overstay etc is just erased.

They can’t use the name, because those are not unique in most countries.

Do they use whatever “national identification number” that’s available on the passport, if any? Then what if some countries don’t have that, or it’s not printed on the passport?

Or do they have some global computer system, where they can search on a passport number, and get all other passport numbers connected to that individual? This would seem like the most sensible option, but I can’t find any information about such a system.

Note that I’m not asking specifically about the system that the USA is using. I’m thinking more like in general, since this must be a problem that every country faces to some degree.